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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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If Y1 and Y2 are independent exponential random variables,

Chapter 6, Problem 13E

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QUESTION:

If \(Y_{1} \text { and } Y_{2}\) are independent exponential random variables, both with mean \(\beta\), find the density function for their sum. (In Exercise 5.7, we considered two independent exponential random variables, both with mean 1 and determined \(P\left(Y_{1}+Y_{2} \leq 3\right)\)

Equation Transcription:

Text Transcription:

Y_1 and  Y_2

\beta

P(Y_1+Y_2 \leq 3)

Questions & Answers

QUESTION:

If \(Y_{1} \text { and } Y_{2}\) are independent exponential random variables, both with mean \(\beta\), find the density function for their sum. (In Exercise 5.7, we considered two independent exponential random variables, both with mean 1 and determined \(P\left(Y_{1}+Y_{2} \leq 3\right)\)

Equation Transcription:

Text Transcription:

Y_1 and  Y_2

\beta

P(Y_1+Y_2 \leq 3)

ANSWER:

Solution 13E

Step1 of 2:

Let us consider independent exponential random variables , both have mean

We need to find the density function for their sum.

Step2 of 2:

The exponential density function with mean is:

         

Since are independent, the density function is the product of the marginal density functions:

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