# Probability and Statistics Questions and Answers – Probability Distributions – 1

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This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Probability Distributions – 1”.

1. 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: None.

2. 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.

3. 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: None.
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4. 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.

5. 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.

6. 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.

7. 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.

8. If a variable can certain integer values 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 discrete random variable.

9. The expected value of a discrete random variable ‘x’ is given by ___________
a) P(x)
b) ∑ P(x)
c) ∑ x P(x)
d) 1

Explanation: Expected value refers to mean which is given by http://mathurl.com/zqymzn7 in case of discrete probability distribution.

10. If ‘X’ is a continuous random variable, then the expected value is given by ___________
a) P(X)
b) ∑ x P(x)
c) ∫ X P(X)
d) No value such as expected value

Explanation: Since X is a continuous random variable, its expected value is given by c.

11. Out of the following values, which one is not possible in probability?
a) P(x) = 1
b) ∑ x P(x) = 3
c) P(x) = 0.5
d) P(x) = – 0.5

Explanation: In probability P(x) is always greater than or equal to zero.

12. If E(x) = 2 and E(z) = 4, then E(z – x) =?
a) 2
b) 6
c) 0
d) Insufficient data

Explanation: E(z – x) = E(z) – E(x)
= 4 – 2 = 2.

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