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Questions › JNU › JNU SIS 2018 › Q22
2 marks, −1Statistics › Random variables and standard distributions › Exponential and gamma distributionsModerateabout 3 min

JNU SIS 2018 Question 22: Random variables and standard distributions

A random variable XXX has the following cumulative distribution function :

F(x)={1−e−x−xe−xfor 0≤x<∞0elsewhereF(x) = \begin{cases} 1 - e^{-x} - xe^{-x} & \text{for } 0 \le x < \infty \\ 0 & \text{elsewhere}\end{cases}F(x)={1−e−x−xe−x0​for 0≤x<∞elsewhere​

The mean and the mode of this distribution are

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A random variable X has the following cumulative distribution function: F(x) = { 1 - e^(-x) - xe^(-x) for 0 ≤ x < ∞; 0 elsewhere } The mean and the mode of this distribution are (A) mean = 0, mode = 0 (B) mean = 2, mode = 1 (C) mean = 2, mode = 0 (D) mean = 1, mode = 2

Also written as: A random variable X has the following cumulative distribution function: F(x) = { 1 - e^(-x) - xe^(-x) for 0 <= x < inf; 0 elsewhere } The mean and the mode of this distribution are

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Exponential and gamma distributions, part of Random variables and standard distributions in Statistics.

Waiting times, memorylessness and sums of exponentials.

TestStop has 7 past-paper questions on this subtopic.

Practise Random variables and standard distributionsMore on Exponential and gamma distributions

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Question from the JNU SIS 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.