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) λ^{2}

d) 1/λ^{2}

View Answer

Explanation: The mean of Exponential distribution is given as 1/λ and variance as 1/λ

^{2}.

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

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

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

View Answer

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(e

^{0}– 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

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}.

**Sanfoundry Global Education & Learning Series – Probability and Statistics.**

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