1. If E denotes the expectation the variance of a random variable X is denoted as?
a) (E(X))2
b) E(X2)-(E(X))2
c) E(X2)
d) 2E(X)
Explanation: By property of Expectation
V (X) = E (X2)-(E(X))2.
2. X is a variate between 0 and 3. The value of E(X2) is ______
a) 8
b) 7
c) 27
d) 9
Explanation: Integrating f(x) = x2 from 0 to 3 we get E(X2) = 32 = 9.
3. The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. The variance of Z is?
a) 3
b) 4
c) 5
d) 7
Explanation: Var(X) = 0.2, Var(Y) = 0.5
Z = 5X – 2Y
Var(Z) = Var(5X-2Y)
= Var(5X) + Var(2Y)
= 25Var(X) + 4Var(Y)
Var(Z) = 7.
4. Which of the following mentioned standard Probability density functions is applicable to discrete Random Variables?
a) Gaussian Distribution
b) Poisson Distribution
c) Rayleigh Distribution
d) Exponential Distribution
Explanation: Poisson Distribution
5. What is the area under a conditional Cumulative density function?
a) 0
b) Infinity
c) 1
d) Changes with CDF
Explanation: Area under any conditional CDF is 1.
6. When do the conditional density functions get converted into the marginally density functions?
a) Only if random variables exhibit statistical dependency
b) Only if random variables exhibit statistical independency
c) Only if random variables exhibit deviation from its mean value
d) If random variables do not exhibit deviation from its mean value
Explanation: Only if random variables exhibit statistical independency
7.Mutually Exclusive events ___________
a) Contain all sample points
b) Contain all common sample points
c) Does not contain any sample point
d) Does not contain any common sample point
Explanation: Events are said to be mutually exclusive if they do not have any common sample point.
8. What would be the probability of an event ‘G’ if H denotes its complement, according to the axioms of probability?
a) P (G) = 1 / P (H)
b) P (G) = 1 – P (H)
c) P (G) = 1 + P (H)
d) P (G) = P (H)
Explanation: According to the given statement P(G) + P(H) = 1.
9. A table with all possible value of a random variable and its corresponding probabilities is called ___________
a) Probability Mass Function
b) Probability Density Function
c) Cumulative distribution function
d) Probability Distribution
Explanation: The given statement is the definition of a probability distribution.
10. A variable that can assume any value between two given points is called ___________
a) Continuous random variable
b) Discrete random variable
c) Irregular random variable
d) Uncertain random variable
Explanation: This is the definition of a continuous random variable.