Probability and Statistics Questions and Answers – Exponential Distribution

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This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Exponential Distribution”.

1. The mean of exponential distribution is given as __________
a) 1/λ
b) λ
c) λ2
d) 1/λ2

Explanation: The mean of Exponential distribution is given as 1/λ and variance as 1/λ2.
E(X)=1/λ.

2. A mobile conversation follows a exponential distribution f (x) = (1/3)e-x/3. What is the probability that the conversation takes more than 5 minutes?
a) e-5/3
b) e-15
c) 5e-15
d) e-5/3

Explanation: f(x) = (1/3)e-x/3. The call should last more than 5 minutes so integrating from 5 till infinity we get
$$\frac{1}{3} ∫ (e^{-x/3}dx) = \frac{1}{3}(\frac{- e^{-5/3}}{-1/3})$$
= e-5/3.

3. Exponential distribution is bi-variate.
a) True
b) False

Explanation: Exponential distribution is uni-variate.
It is only defined for non-negative variables.

4. A random variable X has an exponential distribution with probability distribution function is given by
f(x)= 3e-3x for x>0 = 0 otherwise
Find probability that X is not less than 2.
a) e-3
b) e-6 – 3
c) e-6
d) e-6 – 1

Explanation: Probability of the function taking values from 2 to infinity.
P(X > 2) = 1 – P(X < 2) = Integrating the function from 0 to 2 we get
P(X = 1) = 1 – [3(e0 – e-6)/(-3)]
= e-6.

5. Consider a random variable with exponential distribution with λ=1. Compute the probability for P (X>3).
a) e-3
b) e-1
c) e-2
d) e-4

Explanation: The function takes values from 3 to infinity. This can be written alternatively as integrating from 0 to 3 and subtracting the whole from
P(X > 3) = 1 – P(X < 3)
= 1 – (1 – e-3)
= e-3.

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