1- Number of heads when when we toss some coins is an example of: ?
(A) Discrete Random Variable (B) Continuous Random Variables
Option (A) is correct.
Note: Must remember that Discrete Random Variable has Countable Number of Values. But, Continuous Random Variable has Uncountable Number of Values. Here, Option (A) is correct because we can count "Number of Heads when we toss 2 or more coins.
2- Lengths, Widths is an example of: ?
(A) Discrete Random Variable (B) Continuous Random Variable
Option (B) is correct.
3- A variable which can assume values of random experiment is called as:
(A) Random Variable (B) Random Experiment
Option (A) is correct.
4- Probability Distribution is also called as:
(A) Distribution Function (B) Probability Mass Function
Option (B) is correct.
Note: Q- What is Probability Distribution?
An arrangement of probabilities against each possible value of discrete random variable is called as Probability Distribution.
5- Distribution Function , F(x) =: ?
(A) P(X<x) (B) f(x)
Option (A) is correct.
Note: In reality, P(X<x) that is; Probability of ( X less than and equal to x).
6- Distribution Function is also defined as: ?
(A) Cumulative Probability Distribution (B) Probability Mass Function
Option (A) is correct.
7- Probability Density Function is always: ?
(A) Discrete (B) Continuous
Option (B) is correct.
Note: Probability Density function is denoted as " f(x)" .
8- Expectation E(X) = ?
(A) Sum of X.P(X) (B) Nothing
Option (A) is correct.
9- E(aX + b) =: ?
(A) aE(X) + b (B) E(x) + b
Option (A) is correct.
Note: Must remember that Most Important point which nobody tells you about that, " Mean = Expectation ". Next, Mean of "a" = E(a) = a. that is; Expectation of a constant value is equal to constant itself.
10- Probability Distribution for only two variables at a time is called as: ?
(A) Bi-Variate Probability Distribution (B) Joint Probability Distribution
Option (A) is correct.
Note: But, Probability Distribution for two or more than two variables is called as Joint Probability Distribution. Must focus on that point " Bi-Variate Probability Distribution = Joint Probability Distribution because both distributions have two variables. When we check that it has three variables then it must be purely 'Joint Probability Distribution' .
11- Two random variables X and Y will be Independent If: ?
(A) f(X,Y) = g(X).h(Y) (B) f(X,Y) = f(X)
Option (A) is correct.
Note: But, If two random variables X and Y will be Dependent then " f(X,Y) does not equal to g(X).h(Y).
12- Covariance of X and Y ; Cov(X,Y) and Correlation Coefficient are zero, When
(A) X and Y are Independent (B) X and Y are Dependent
Option (A) is correct.
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