Exponential Distribution Questions and Answers

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
View Answer

Answer: a
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
View Answer

Answer: a
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
View Answer

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

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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
View Answer

Answer: c
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
View Answer

Answer: a
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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