Can You Solve Amazon's Hanging Cable Interview Question ? | Hanging Cable Problem | Amazon Interview Preparation | 2021

 

Can You Solve Amazon’s Hanging Cable Interview Question?

THAT'S A MOST IMPORTNT AMAZON INTERVIEW QUESTION WHICH MOSTLY ASKED IN INTERVIEW: 

A cable of 80 meters (m) is hanging from the top of two poles that are both 50 m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:

(a) 20 m above the ground?
(b) 10 m above the ground?

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GENERAL CATENARY EQUATION IS:

Y = a Cosh(x/a) - a

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Components of Time Series with Examples (Real life Examples) | Easiest & Shortcuts | PDF 2021

 QUESTIONS WITH ANSWERS:

What is Time Series?

Arrangement of data according to time period is called as Time Series.

                                               OR

Cronological arrangement of data is defined as Time Series.

What are the Components of Time Series?

REASONS:

Reasons of fluctuations (Ups and Downs) in Time Series are the components of time series.

COMPONENTS OF TIME SERIES:

There are Four Components of Time Series:

1 - Secular Variations (Trend)

2 - Seasonal Variations

3 - Cyclic Variations 

4 - Irregular Variations

What are the Secular Variations?

The Variations which are very long term and which may covers more than 10 years to occur are known as Secular Variations. These are slow and gradual changes.

REAL LIFE EXAMPLE:

The transport system in old time is converted into the modern transport system and it took very long time to change.

What are the Seasonal Variations?

The Variations which are caused by Seasons, Religious festivals and our Traditions are called as Seasonal Variations. These changes reoccur after the fix interval of time.

EXAMPLE:

Great demand of warm clothes near winter.

What are the Cyclic Variations?

The Variations which are long term oscillations and which are like swings or waves type movements are called as Cyclic Variations.

Most Important Real Life Example:

The main example of Cyclic Variations is the life of a business man.

There are four Stages in the life of a business man:

1 - Prosperity

2 - Contraction (Recession)

3 - Depression (Trough)

4 - Recovery 

What are the Irregular Variations?

The Variations which are due to accidental events or random events like floods, earthquakes, famines, wars.

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Difference between Multiple Correlation and Partial Correlation (PDF) 2020 Vs 2021

 Difference between Multiple Correlation Coefficient and Partial Correlation Coefficient:

MULTIPLE CORRELATION:

Multiple Correlation is the relationship between a Variable and a Combined Variable.

MULTPLE CORRELATION COEFFICIENT:

The Coefficient of a Multiple Correlation measures the degree of relationship between a variable and its estimate from the regression equation.

REPRESENTATION:

It is represented as...

FORMULA:

PARTIAL CORRELATION:

The relationship between any two variables by neglecting the effect of other variable is called as Partial Correlation.

PARTIAL CORRELATION COEFFICIENT:

The coefficient of a partial correlation measures the degree of linear relationship between any two variables in a multivariate problem under the condition that any common relationship with all other variables has been removed.

REPRESENTAION:

It is represented as...

FORMULA:

NOTE:

We know that

r XY is...

then r12 will be as...

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What are the 5 Main Properties of Correlation Coefficient? (PDF) 2021

 PROPERTIES OF CORRELATION COEFFICIENT ' r ' :

1 - Correlation Coefficient 'r' lies between - 1 and + 1 , that is; - 1 <  r < + 1 .

2 - Correlation Coefficient 'r' is Symmetric about X and Y....

                                  r XY = r YX

The Formula of Correlation Coefficient ' r ' is.....

3 - Correlation Coefficient  ' r ' is the Geometric Mean of two Regression Coefficients.

REGRESSION COEFFICIENTS:

There are Two regression coefficients : 

b YX; 

b XY;

NOTE: The Main Common formulas of Regression Coefficients are: 

b YX;

b XY;

4 - Correlation Coefficient 'r' in Independent of change of origin and scale, that is;

                                              r XY = r UV

But the Formula of  " r UV " is:

5 - Correlation Coefficient 'r' is the Independent of any unit of measurement.

MOST IMPORTANT POINTS:

The Regression line Y on X is...

The Regression line X on Y is...

At last,

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Correlation | Correlated | Positive Correlation | Negative Correlation | Correlation Coefficient & Formula | Rank Correlation & Coefficient

 QUESTIONS WITH ANSWERS: Simple & Easiest with Real life Examples 2021

What is Correlation?

Relationship between two Variables is called as Correlation.

For Example, We can say Married Persons " Relationship between Husband and Wife ".

What is Correlated?

The movement of one variable is accompanied by the movement of other variable is called as Correlated.

For Example, Let's  take an example of Cars; We have Two Cars, We bind the One Car with the other Car by a rope then you can noticed that When One Car will move then automatically other car will move. That's relation is CORRELATED. It is denoted by " r ".

What is the Difference between Positive Correlation and Negative Correlation?

STEP-BY-STEP:

What is Positive Correlation?

When movement of two variables is in same direction that is both variables may increase or both decrease is called as Positive Correlation.

For Example, let's suppose that two persons have own bikes and they are racing in same direction then obviously both persons speed may increase or decrease. That's is a Positive Correlation.

NOTE: The value of 'r' will be positive When r = + 1, Correlation is perfect positive.

What is Negative Correlation?

When movement of two variables are in opposite direction then Correlation will be negative.

For Example, let's suppose there are two persons; One is going to the right side and other is going to the left side which shows that they have not any relationship. So, correlation will be negative.

NOTE: The value of 'r' will be negative When r = - 1, Correlation is perfect negative.

What is Correlation Coefficient or Coefficient of Correlation?

The Strength of relationship between two variables is measured by the formula which is named as Correlation Coefficient. It is denoted by 'r'.

General Formula:

Where

Co-variance of X and Y formula is:

Variance of X and Y formula is:

Now, at last..

Common Formula: 

That's common formula is a main formula which we use in calculation of 'r'.

What is Rank Correlation?

When actual values of two variables are ranked according to some common characteristics then Correlation will be Rank Correlation.

What is the Coefficient of Rank Correlation?

The Coefficient of Rank Correlation is: 

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Coefficient of Determination & its Formula | Explained Variation | Unexplained Variation | Total Variation 2021

 COEFFICIENT OF DETERMINATION:

DEFINITION:

The Ratio of  Explained Variation to the Total Variation is called as Coefficient of Determination.

It is denoted as above "r square".

                   Coefficient of Determination = Explained Variation/Total Variation

Where

What is Explained Variation?

Explained Variation is...

&

What is Total Variation?

Total variation is...

So, we can write Coefficient of Determination Formula also as...

NOTE: Coefficient of Determination may also be written as...

             Coefficient of Determination = 1 - Unexplained Variation/Total Variation

What is Unexplained variation?

Unexplained Variation is...

So, Coefficient of Determination Formula will become...

It may also be written as...

Most Important Information:

Total Variation = Explained Variation + Unexplained Variation

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How to Make Easy Theory of Simple Linear Regression (PDF) 2021

 I have discussed here theory of REGRESSION STEP-BY-STEP with #secrets #shortcuts #concepts which nobody tells you about that.!

SEQUENCE: REGRESSION; REGRESSION EQUATION; REGRESSOR; REGRESSAND; EXACT RELATIONSHIP; INEXACT RELATIONSHIP; STANDARD ERROR OF ESTIMATE OF REGRESSION(STANDARD DEVIATION OF REGRESSION).

QUESTIONS WITH ANSWERS:

WHAT IS REGRESSION?

Dependence of One Variable on other Independent Variable is called as REGRESSION.

WHAT IS REGRESSION EQUATION?

An Equation which estimates the value of Dependent Variable with the help of Independent Variable by knowing the values of unknown parameters is called as REGRESSION EQUATION.

                                                          REGRESSION EQUATION

Y on X                                                          X on Y                                                                             

Y = a + b X                                        X = a + b Y                                                                                     

Y is Dependent Variable,                      X is Dependent Variable                                                             

X is Independent Variable,                   Y is Independent Variable                                                              

WHAT IS THE DIFFERENCE BETWEEN REGRESSOR AND REGRESSAND?

WHAT IS THE DIFFERENCE BETWEEN PREDICTOR AND PREDICTAND?

WHAT IS THE DIFFERENCE BETWEEN EXPLANATORY VARIABLE AND EXPLAINED VARIABLE?

The Independent Variable is called as REGRESSOR or PREDICTOR or EXPLANATORY VARIABLE.

The Dependent Variable is called as REGRESSAND or PREDICTAND or EXPLAINED VARIABLE.

WHAT IS THE DIFFERENCE BETWEEN EXACT RELATIONSHIP AND INEXACT RELATIONSHIP?

WHAT IS THE DIFFERENCE BETWEEN MATHEMATICAL RELATIONSHIP AND PROBABILISTIC RELATIONSHIP & ESTIMATED RELATIONSHIP?

Exact Relationship or Mathematical Relationship:

A Relationship which calculates the value of one Variable Exactly with the help of other Variable is called as Estimated Relationship or Mathematical Relationship.

For Example,

Inexact Relationship or Probabilistic Relationship or Estimated Relationship:

A Relationship which estimates the value of one Variable (Dependent Variable) with the help of other Variable (Independent Variable) is called as Inexact Relationship or Probabilistic Relationship or Estimated Relationship.

For Example, The Relationship between Age and Weight.

DEFINE STANDARD DEVIATION OF REGRESSION or STANDARD ERROR OF ESTIMATE OF REGRESSION?

Positive Square Root of Mean of Squared Deviation from Estimated Trend Values from Regression Equation is called as Standard Deviation of Regression or Standard Estimate for Regression.

For Y on X                                   Y = a + b X

& 

For X on Y                                   X = a + b Y

&

Most Important Point;

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Nonparametric Tests Multiple Choice Questions and answers (mcqs)

 1- Nonparametric Tests referred to as _ : ?

(A) Distribution-free test      (B) Z-test

Option (A) is correct.

2- We always use _ when the mean more accurately the center of distribution of your data and sample size is large enough: ?

(A) Parametric Test             (B) Nonparametric Test

Option (A) is correct.

3- If the Median more accurately represents the center of distribution of your data, use a _ even If you have a large size: ?

(A) Nonparametric Test      (B) Parametric Test

Option (A) is correct.

4- Chi-Square test is a _ : ?

(A) Parametric Statistic      (B) Nonparametric Statistic

Option (B) is correct.

5- T-Tests or Z-Tests are a type of _ method: ?

(A) Parametric                    (B) Nonparametric

Option (A) is correct.

6- The nonparametric tests may be applied to _ data or data that can be ranked but not measured exactly: ?

(A) Quantitative                 (B) Qualitative

Option (B) is correct.

7- Nonparametric Tests are generally _ : ?

(A) Less Efficient              (B) More Efficient

Option (A) is correct.

8- Nonparametric tests require a _ sample size than do the corresponding parametric tests: ?

(A) Larger                         (B) Smaller

Option (A) is correct.

9- Sign test is used to test the _ : ?

(A) Alternative Hypothesis   (B) Null Hypothesis

Option (B) is correct.

10- Analysis of Variance (ANOVA) is: ?

(A) Parametric                      (B) Nonparametric

Option (A) is correct.

11- Rank Correlation is: ?

(A) Nonparametric              (B) Parametric

Option (A) is correct.

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Statistical Inference in Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- Fisher's z-transformation is denoted as: ?

(A) Zf                                 (B) F

Option (A) is correct.

2- The Process of analysing the total variation in the dependent variable Y into its components; one explained by regression line and the other residual or unexplained part is defined as: ?

(A) Analysis of Variance for Regression (B) ANCOVA

Option (A) is correct.

3- Total SS(Sum of Squares) =: ?

(A) Within SS + Between SS   (B) Residual or Error SS(SSE) + Regression SS(SSR)

Option (B) is correct.

4- In ANOVA for Multiple Regression and Testing Hypothesis about the "beta" parameters, degrees of freedom are: ?

(A) V1 = 2, V2 = n - 3            (B) V1 = k - 1, V2= n - k

Option (A) is correct.

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Experimental Designs Multiple Choice Questions and answers (mcqs)

 1- Experimental Design means _ used to collect the data: ?

(A) Plan                                (B) Designing

Option (A) is correct.

2- The Purpose of randomization is to _ bias and other sources of extraneous variation: ?

(A) Accept                             (B) Remove

Option (B) is correct.

3- A term reffering  to the amount of balancing, blocking and grouping of the experimental units is called as: ?

(A) Local Control                  (B) Replication

Option (A) is correct.

4- A Completely Randomized Design (CR) design is also called as: ?

(A) One-Way ANOVA           (B) Two-way ANOVA

Option (A) is correct.

5- A Randomized Complete Block Design (RCB) is also defined as: ?

(A) Two-Way ANOVA           (B) One-Way ANOVA

Option (A) is correct.

6- A Replication is used to secure more accurate estimate of the _ : ?

(A) Repetition                        (B) Experimental Error

Option (B) is correct.

7- A Replication is used to _ the experimental error and thereby to increase precision: ?

(A) Increase                            (B) Decrease

Option (B) is correct.

8- A Completely Randomized (CR) design is one in which treatments are assigned to experimental units completely _ : ?

(A) At Random                       (B) At Most

Option (A) is correct.

9- In CR Design, There is possibility of entering the whole of the variation among the experimental units into the _ as the randomization is not restricted in any direction: ?

(A) experimental error            (B) Design 

Option (A) is correct.

10- Complete Randomized Block (RCB) Design controls variability only in: ?

(A) 3 direction                        (B) 1 direction

Option (B) is correct.

11- Latin Square (LS) Design is also called as: ?

(A) Two-way ANOVA            (B) Three-way ANOVA

Option (B) is correct.

12- In Latin Square (LS) Design, treatments are grouped in blocks in: ?

(A) Two directions                  (B) One direction

Option (A) is correct.

13- In Latin Square Design, Rows, Columns and Treatments are always: ?

(A) Not Equal                          (B) Equal

Option (B) is correct.

14- In Latin Square (LS) Design , the degree of freedom, V2 is the: ?

(A) Error Degree of Freedom   (B) Nothing

Option (A) is correct.

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Analysis of Covariance (ANCOVA) Multiple Choice Questions and answers (mcqs)

 1- Analysis of Covariance is abbreviated as: ?

(A) ANCOVA                        (B) ANOVA

Option (A) is correct.

Note: But, ANOVA shows here Analysis of Variance.

2- ANCOVA is a blending of ANOVA and _: ?

(A) Regression                       (B) Correlation

Option (A) is correct.

3- Control Variables are called as: ?

(A) Correlated                        (B) Covariates

Option (B) is correct.

4- ANCOVA has a _ Continuous Response Variable: ?

(A) Double                             (B) Single

Option (B) is correct.

5- Concomitant Variable or Covariate is denoted as: ?

(A) X                                       (B) Y

Option (A) is correct.

6- In ANCOVA, the Populations are Normally distributed with _ Variances: ?

(A) Homogeneous                   (B) Heterogeneous

Option (A) is correct.

7- The Covariance adjustments remove the _ due to regression: ?

(A) Covariates                         (B) Bias

Option (B) is correct.

8- In ANCOVA, the regression is _ and the slope is not _ : ?

(A) Quadratic, 1                       (B) Linear, Zero

Option (B) is correct.

9- In ANCOVA, Treatment, Block and Regression effects are _ : ?

(A) Additive                              (B) Multiplicative

Option (A) is correct.

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Analysis of Variance (ANOVA) Multiple Choice Questions and answers (mcqs)

 1- The Analysis of Variance is abbreviated as: ?

(A) ANOVA                         (B) ANCOVA

Option (A) is correct.

2- Analysis of Variance is introduced by: ?

(A) Sir R.A. Fisher              (B) G.W Snedecor

Option (A) is correct.

3- For Testing more than two Means, we always use: ?

(A) t-distribution                  (B) Analysis of Variance(ANOVA)

Option (B) is correct.

4- In One-way ANOVA, Total SS(Sum of Squares) =: ?

(A) SSR + SSC + SSE         (B) Within SS + Between SS

Option (B) is correct.

5- Within SS(Sum of Squares) is also called as: ?

(A) Error SS                         (B) Between SS

Option (A) is correct.

6- In Analysis of Variance , the more the sample means differ the _ the variance becomes: ?

(A) Smaller                           (B) Larger

Option (B) is correct.

7- The Analysis of Variance compares two different estimates of variance by using F-distribution to determine whether the Population Means are: ?

(A) Equal                               (B) Not Equal

Option (A) is correct.

Note; Must remember that  in Null Hypothesis " Ho : All means are equal".

8- In One-way ANOVA, Columns "c" is also equal to: ?

(A) k                                      (B) f

Option (A) is correct.

9- In One-way ANOVA, degrees of freedom are: ?

(A) V1 = k - 1  ,  V2 = n - k       (B) V1 = r - 1,   V2 = (r - 1)(c - 1)

Option (A) is correct.

Note: But, In Two-way ANOVA, degrees of freedom are V1 = r - 1, V2 = (r - 1)(c - 1) & also V1 = c - 1,   V2= (r - 1)(c - 1).

10- In Two-way ANOVA, Total SS (SST) =: ?

(A) SSR + SSC + SSE                (B) Within SS + Between SS

Option (A) is correct.

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F-Distribution Multiple Choice Questions and answers (mcqs)

 1- Two normally distributed populations having Equal Variances is defined as: ?

(A) F-Distribution                      (B) Z-Distribution

Option (A) is correct.

2- F-Distribution has shape as same as the shape of: ?

(A) Chi-Square                          (B) Normal 

Option (A) is correct.

3- The Range of F-Distribution is from: ?

(A) - infinity to + infinity          (B) 0 to infinity

Option (B) is correct.

Note: Chi-Square also have a Range from '0 to infinity'.

4- F-Distribution has _ skewness: ?

(A) Negative                             (B) Positive

Option (B) is correct.

Note: Must remember that Chi-Square also have a Positive Skewness.

5- F-Distribution approaches Normal Distribution when V1 and V2 (degrees of freedom) becomes: ?

(A) larger                                 (B) Smaller

Option (A) is correct.

6- 1/F has a an F-Distribution with Degrees of Freedom: ?

(A) V1 and V2                         (B) V2 and V1

Option (B) is correct.

7- If V1 = V2, then 1/F is same as that of: ?

(A) F                                        (B) 1/F

Option (A) is correct.

8- The Mean of the F-Distribution with V1 and V2 degrees of freedom are: ?

(A) V2/V2 - 2  for V2 > 2        (B) V2/V1

Option (A) is correct.

9- F-distribution can be applied If the two samples are _ and randomly selected: ?

(A) Dependently                      (B) Independently

Option (B) is correct.

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Student's t-distribution Multiple Choice Questions and answers (mcqs)

 1- In Student's t-distribution, Degree of Freedom "v" =: ?

(A) n - 1                       (B) m - 1

Option (A) is correct.

2- The shape of t-distribution is: ?

(A) Bell Shaped         (B) Square Shaped

Option (A) is correct.

Note: Must remember that also the shape of Normal Distribution "Z" is bell shaped.

3- t-distribution has range from: ?

(A) 0 to infinity         (B) - infinity to + infinity

Option (B) is correct.

Note: Also Normal Distribution 'Z' has range from " - infinity to + infinity ".

4- t-distribution has shape as same as the shape of: ?

(A) Chi-Square         (B) Normal Distribution

Option (B) is correct.

5- The Variance of t-distribution is: ?

(A) v/v - 2                (B) v/2

Option (A) is correct.

6- t-distribution approaches to the normal distribution as 'V' or size 'n' becomes: ?

(A) Larger               (B) Smaller

Option (A) is correct.

7- The Mean of the t-distribution is Zero, when: ?

(A) v < 2                 (B) v > 2

Option (B) is correct.

Note: The Mean is undefined for v = 1.

8- 'SP' of Student's t-distribution have_ formulae: ?

(A) three                 (B) four

Option (A) is correct.

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Chi Square Distribution Multiple Choice Questions and answers (mcqs)

 1- Chi-Square Distribution has Range from: ?

(A) - infinity to + infinity    (B) 0 to infinity

Option (B) is correct.

2- The Curve of a Chi-Square Distribution is _ Skewed: ?

(A) Positively         (B) Negatively

Option (A) is correct.

3- Chi-Square Distribution tends to Normal Distribution as the number of degree of freedom approaches: ?

(A) Infinity             (B) Zero

Option (A) is correct.

4- In Test of Independence, alpha means: ?

(A) not B                 (B) not A

Option (B) is correct.

5- Attribute is also called as: ?

(A) Qualitative Variable  (B) Quantitative Variable

Option (A) is correct.

6- If Co-efficient of Association, Q=1, then Attributes are: ?

(A) Disassociated            (B) Completely Associated

Option (B) is correct.

7- The Range of Co-efficient of Association lies between: ?

(A) - 1 and + 1                (B) 0 to infinity

Option (A) is correct.

8- Associated means: ?

(A) Independent             (B) Not Independent

Option (B) is correct.

9- If (AB) = (A) (B)/n, then Attributes A and B are called as: ?

(A) Associated               (B) Independent

Option (B) is correct.

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Hypothesis Testing Multiple Choice Questions and answers (mcqs)

 1- Type - I Error is made by Rejecting of Ho If Ho is: ?

(A) True                   (B) False

Option (A) is correct.

Note: But, must remember that Type - II Error is made by Accepting of Ho If Ho is False.

2- Which of the following is not the Simple Hypothesis: ?

(A) Ho : Mean = 60        (B) H1 : Mean > 60

Option (B) is correct.

Note: Simple Hypothesis is One in which all the parameters of the distribution are specified. For Example, Ho: Mean=60.

3- Rejection Region is also called as: ?

(A) Critical Value            (B) Critical Region

Option (B) is correct.

4- Power of Test =: ?

(A) 1 - alpha             (B) 1 - betta

Option (B) is correct.

5- Level of Significance is denoted as: ?

(A) alpha                   (B) betta

Option (A) is correct.

6- Most Common Values of alpha are: ?

(A) 5 %  or 1 %        (B) 2 % or 3 %

Option (A) is correct.

7- Test-statistic is a: ?

(A) Value                  (B) Formula

Option (B) is  correct.

Note: Test-statistic is a sample statistic or formula which provides a basis for testing the null hypothesis.

8- If Ho is Rejected after testing is called as: ?

(A) Insignificant Testing    (B) Significant Testing

Option (B) is correct.

Note: But, If Ho is Accepted after testing is called as Insignificant Testing.

9- Type - I Error is denoted by: ?

(A) alpha            (B) betta

Option (A) is correct.

Note: But, Type - II Error is denoted as 'betta'.

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Statistical Inference Multiple Choice Questions and answers (mcqs)

 1- Discussion about Population Parameter on the basis of Sample Observations is called as: ?

(A) Statistical Inference       (B) Inferential Statistics 

Option (A) is correct.

2- The Estimator is defined as: ?

(A) Formula             (B) Value

Option (A) is correct.

Note: But, Estimate is a Value.

3- An Estimator would be Consistent If Variance of this Estimator becomes _  as n approaches infinity: ?

(A) Nine                  (B) Zero

Option (B) is correct.

4- If Efficiency > 1, then T is _ efficient: ?

(A) More                 (B) Less

Option (A) is correct.

5- T1 will be more efficient than T2 If: ?

(A) Var (T1) > Var(T2)     (B) Var(T1) < Var(T2)

Option (B) is correct.

6- BLUE is abbreviated as: ?

(A) Best Linear Unbiased Estimator   (B) Blue Light Union Enter

Option (A) is correct.

7- In BLUE, Variance is always: ?

(A) Least                (B) at most

Option (A) is correct.

8- Level of Confidence is: ?

(A) alpha                (B) 1 - alpha

Option (B) is correct.

9- Confidence Coefficient is always: ?

(A) ( 1 - alpha ) 100 %   (B) 1 - alpha

Option (A) is correct.

10- Is an Estimator a Random Variable: ?

(A) No                     (B) Yes

Option (B) is correct.

Note: Yes, Estimator is a random variable because Estimator has different Probability Distributions.

11- For Checking the Unbiasedness of Estimators T1 and T2, we should take: ?

(A) Expectation         (B) Variance

Option (A) is correct.

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Survey Sampling and Sampling Distributions Multiple Choice Questions and answers (mcqs)

 1- Sample is a part of: ?

(A) Population      (B) Proportion

Option (A) is correct.

2- If n < 5% of N, then we always use: ?

(A) With Replacement (B) Without Replacement 

Option (A) is correct.

Note: If n > 5% of N, then we always use Without Replacement.

3- Sample Proportion 'p' =: ?

(A) X/N                 (B) x/n

Option (B) is correct.

Note : Must remember that Population Proportion 'P' = X/N.

4- Sample Mean is also called: ?

(A) Combined Mean  (B) Geometric Mean

Option (A) is correct.

5- Sampling Error is reduced , when Sample Size 'n': ?

(A) Decreases          (B) Increases

Option (B) is correct.

6- The Systematic Component of error which deprives a survey result of representativeness is defined as: ?

(A) Bias           (B) Sampling Bias

Option (A) is correct.

7- Quota Sample is a Type of: ?

(A) Judgement Sample (B) Sampling Error

Option (A) is correct.

8- Finite Population Correction Factor is: ?

(A) N/n            (B) N-n/N-1

Option (B) is correct.

9- Non-Sampling Errors are: ?

(A) Human Errors   (B) Bias

Option (A) is correct.

10- Method to select suitable sample from population is called as: ?

(A) Sample Mean       (B) Sampling

Option (B) is correct.

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Time Series Multiple Choice Questions and answers (mcqs)

 1- Arrangement of data according to time period is called as: ?

(A) Time Series         (B) Seasonal Variation

Option (A) is correct.

2- Graph of Time Series in which Time period is taken along x-axis and Values along y-axis is called as: ?

(A) Histogram          (B) Historigram

Option (B) is correct.

Note: But, Histogram: Graph of Adjacent Rectangles in which Class Boundaries are taken along x-axis and frequency along y-axis is called as Histogram.

3- Ups and Downs (Fluctuations) in Time Series are: ?

(A) Components of Time Series   (B) Irregular Variations

Option (A) is correct.

4- TCSI abbreviated as: ?

(A) Secular Trend; Cyclic; Seasonal; Irregular  (B) Nothing

Option (A) is correct.

5- The Variations which are caused by Religious Festivals, and Traditions are called as: ?

(A) Cyclic Variations   (B) Seasonal Variations

Option (B) is correct.

6- The life of a Buisness man is an Example of: ?

(A) Cyclic Variations   (B) Secular Trend

Option (A) is correct.

7- The Process of removing trend from time series is defined as: ?

(A) Deseasonalization  (B) Detrending

Option (B) is correct.

Note: Must remember that the process of removing seasonal effect from time series is called as Deseasonalization.

8- From Additive Model; Y = T + C + S + I, we can isolate any component by: ?

(A) Method of Subtraction (B) Method of Division 

Option (A) is correct.

Note: But, From Multiplicative Model; Y = TCSI, we can isolate any component by the Method of Division. For example, Y = TCSI/C = TSI.

9- Parabola is always has: ?

(A) Second Degree          (B) First Degree

Option (A) is correct.

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Curve Fitting by Least Squares Multiple Choice Questions and answers (mcqs)

 1- A linear Curve is: ?

(A) Y = a + b X       (B) Y = ab

Option (A) is correct.

Note: You already know that ' Y = a + b X ' is also a Regression line.

2- The Equation of Hyperbola is: ?

(A) 1/B = X            (B) 1/Y = a + b X

Option (B) is correct.

3- We fit an Exponential Curve If the first differences of the Logarithms are approximately: ?

(A) Constant          (B) Variable

Option (A) is correct.

4- For better the Fit, The Sum of Squares must be: ?

(A) Bigger              (B) Smaller 

Option (B) is correct.

5- Non-Linear Form is: ?

(A) 1/Y = a + b/1 + X     (B) Y = a + b X

Option (A) is correct.

6- Logistic Curve has _ different Stages: ?

(A) 4                      (B) 3

Option (A) is correct.

Note: Must focus on that's, Logistic Curve has Stages; 1- Period of relatively slow growth, 2- Period of accelerated growth, 3- Period of Decelerated growth, 4- Period of Stability.

7- We Fit a Reciprocal line 1/Y = a + b X, If the reciprocals of data show a _ when plotted in a graph: ?

(A) Regression line     (B) Straight line

Option (B) is correct.

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Multiple Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- The relationship between any two variables by neglecting the effect of other variable is called as: ?

(A) Partial Correlation     (B) Multiple Correlation

Option (A) is correct.

2- The relationship between a Variable and a Combined Variable is called as: ?

(A) Multiple Correlation  (B) Multiple Regression

Option (A) is correct.

3- In Y = a + b1 X1 + b2 X2 ; X1 and X2 are: ?

(A) Dependent Variables  (B) Independent Variables

Option (B) is correct.

Note: Must remember that here "Y" is Dependent Variable.

4- Multiple Correlation Coefficient is denoted by: ?

(A) R1.23               (B) r1.23

Option (A is correct.

5- The Coefficient of Partial Correlation is denoted by: ?

(A) R12.3               (B) r12.3

Option (B) is correct.

6- The Coefficient of Multiple Correlation is denoted as: ?

(A) Ry.12                (B) ry.12

Option (A) is correct.

7- A Regression which have two or more Independent Variables is defined as: ?

(A) Multiple Regression (B) Simple Regression

Option (A) is correct.

Note: But, If Regression have just One Independent Variable is called as Simple Regression.

8- The Coefficient of Multiple Determination lies between: ?

(A) 2 and 3            (B) 0 and 1

Option (B) is correct.

Note: Must focus on that's point ; The Range of Multiple Correlation Coefficient is 0 and 1 also.

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Simple Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- Dependence of one Variable on other Independent Variable is called as: ?

(A) Regression   (B) Correlation 

Option (A) is correct.

Note: Y = a + bX is a Regression Line. Must remember that 'Y' is a Dependent Variable and 'X' is an Independent Variable. Next, 'a' and 'b' are Least-Squares Estimates.

2- The Independent Variable is called as: ?

(A) Regressand    (B) Regressor 

Option (B) is correct.

3- Regressand is also called as: ?

(A) Predictand      (B) Predictor 

Option (A) is correct.

Note: Must note that's points......

Dependent Variable is called as Regressand, Predictand, Explained Variable. But, Independent Variable is called as Regressor, Predictor, Explanatory Variable.

4- Inexact Relationship is also defined as: ?

(A) Mathematical Relationship  (B) Probabilistic Relationship

Option (B) is correct.

5- Explained Variation + Unexplained Variation = ?

(A) Total Variation   (B) Co-efficient of Variation

Option (A) is correct.

6- Relationship between two Variables is called as: ?

(A) Regression      (B) Correlation

Option (B) is correct.

7- When r = +1, then Correlation is: ?

(A) Perfect Positive   (B) Perfect Negative

Option (A) is correct.

Note: But, When r = - 1, then correlation is perfect negative.

8- Correlation Coefficient 'r' lies between: ?

(A) -2 & +2    (B) -1 & +1

Option (B) is correct.

Note: Correlation Co-efficient 'r' is Independent of  change of Origin and Scale.

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Continuous Probability Distributions (Normal Distribution) Multiple Choice Questions and answers (mcqs)

 1- In 52 cards, Diamonds and Spades are: ?

(A) 13       (B) 6

Option (A) is correct.

Note: Ace and kings are 4.

2- Bernoulli's Distribution has range from: ?

(A) 0,1,2,3,.....,n   (B) 0,1

Option (B) is correct.

3- The Mean of Bernoulli's Distribution is: ?

(A) p         (B) pq

Option (A) is correct.

4- A distribution for which probability is same for each value of success is called as: ?

(A) Bernoulli's Distribution (B) Uniform Distribution

Option (B) is correct.

5- The Function of Uniform Distribution is: ?

(A) P(X) = 1/k   (B) P(X) = k

Option (A) is correct.

6- In Sequence, 1 + 2 + 3 +.....+ n =: ?

(A) n/2           (B) n(n+1)/2

Option (B) is correct.

7- The Mean of Uniform Distribution is: ?

(A) k + 1/2      (B) k/2

Option (A) is correct.

8- Poisson Distribution and Normal Distribution are the Limiting Functions of: ?

(A) Binomial Distribution (B) Bernoulli's Distribution

Option (A) is correct.

9- Standard Normal Variable 'Z' is equal to: ?

(A) X/sigma     (B) X - Mean/sigma

Option (B) is correct.

10- Normal Distribution has range from: ?

(A) - infinity to + infinity    (B) 0 to infinity

Option (A) is correct.

11- Mean Deviation of Normal Distribution is: ?

(A) 4/5 sigma or 0.7979 sigma   (B) 2/3 sigma or 0.6745 sigma

Option (A) is correct.

Note: Must remember that Quartile Deviation of Normal Distribution is 2/3 sigma or 0.6745 sigma.

12- The Total Area under Normal Curve is always: ?

(A) 2           (B) 1

Option (B) is correct.

Note: Many people ask that how can we explain " Total area under normal curve is 1".?

Very easy and simple answer :  0.5 + 0.5 = 1.

13- The Shape of Normal Distribution is: ?

(A) Bell Shaped    (B) Square Shaped

Option (A) is correct.

14- Percentage area between Mean - sigma  and Mean + sigma is: ?

(A) 95.45 %       (B) 68.67 %

Option (B) is correct.

Note: But, Percentage area between Mean - 2 sigma and Mean + 2 sigma is 95.45 %. And, Percentage area between Mean - 3 sigma and Mean + 3 sigma is 99.73 %.

15- When sample size "n" is very large and neither "p" nor "q" is very small, that's called as: ?

(A) Normal Distribution   (B Poisson Distribution

Option (A) is correct.

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Discrete Probability Distributions Multiple Choice Questions and answers (mcqs)

 1- All Trials are Independent in: ?

(A) Binomial Experiment (B) Hypergeometric Experiment

Option (A) is correct.

Note: But, all Trials are Dependent in Hypergeometric Experiment.

2- In Binomial Experiment, drawing is done: ?

(A) With Replacement (B) Without Replacement

Option (A) is correct.

Note: But, In Hypergeometric Experiment, drawing is done Without Replacement.

3- Binomial Distribution has range from: ?

(A) 0,1,2,.....infinity (B) 0,1,2,......n

Option (B) is correct.

Note: Must remember that also Hypergeometric Distribution has range from 0,1,2,......n.

4- The Probability of failure 'q' is equal to: ?

(A) 1- p (B) 1-q

Option (A) is correct.

5- The Variance of Binomial Distribution is: ?

(A) npq (B) np

Option (A) is correct.

Note: But, In Binomial Distribution, Mean = np.

6- For Negative Binomial Distribution, Mean and Variance have a relation: ?

(A) Mean > Variance (B) Mean < Variance 

Option (B) is correct.

Note: Must focus on that's, In Binomial Distribution, always Mean > Variance.

7- The Mean of Hypergeometric Probability Distribution is: ?

(A) nk/N (B) npq

Option (A) is correct.

8- In Hypergeometric Probability Distribution, Probability 'p' is equal to : ?

(A) k/N   (B) k/n

Option (A) is correct.

Note: Attention!!

Now, I am going to tell you most Important points which nobody tells you about that. Must remember that In sense of Problems solving, In case of With Replacement , always use the formula of Binomial Distribution. But, In case of Without Replacement , always use the formula of Hypergeometric Distribution.

9- If 'n' becomes very large and the probability of success "p" is very small, then that's type of Distribution is defined as: ?

(A) Normal Distribution (B) Poisson Distribution

Option (B) is correct.

Note : For example, in problems solving,, n=500 and p=0.01. then we always use Poisson Distribution.

10- In Poisson Distribution, Mean and Variance have a relation: ?

(A) Mean = Variance (B) Mean < Variance

Option (A) is correct.

Note: Must remember that In Poisson Distribution, Mean = np and Variance = np.

11- The Product of N and P(X) ; NP(X) is equal to: ?

(A) Expected Frequency (B) Observed Frequency

Option (A) is correct.

12- In Poisson Process, Average number of occurances per unit time is equal to: ?

(A) Lemda (B) t

Option (A) is correct.

Note: t shows 'time interval".

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