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
View Answer

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

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.
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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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn