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Statistics / Mathematical Statistics with Applications 7 / Chapter 6 / Problem 36E

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

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Refer to Exercise 6.34. Let Y1 and Y2 be independent

Chapter 6, Problem 36E

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QUESTION:

Refer to Exercise 6.34. Let \(Y_{1}\) and \(Y_{2}\) be independent Rayleigh-distributed random variables. Find the probability density function for \(U=Y_{1}^{2}+Y_{2}^{2}\) [Hint: Recall Example 6.8.]

Equation Transcription:

${Y}_{1}$

${Y}_{2}$

$U={Y}_{1}^{2}+{Y}_{2}^{2}$

Text Transcription:

Y_1

Y_2

U=Y_1^2+Y_2^2

Questions & Answers

QUESTION:

Refer to Exercise 6.34. Let \(Y_{1}\) and \(Y_{2}\) be independent Rayleigh-distributed random variables. Find the probability density function for \(U=Y_{1}^{2}+Y_{2}^{2}\) [Hint: Recall Example 6.8.]

Equation Transcription:

${Y}_{1}$

${Y}_{2}$

$U={Y}_{1}^{2}+{Y}_{2}^{2}$

Text Transcription:

Y_1

Y_2

U=Y_1^2+Y_2^2

ANSWER:

Solution:

Step 1 of 2:

Let Y1 and Y2 be independent Rayleigh-distributed random variables, with pdf

We have to find the probability density function for U= ${Y}_{1}^{2}+{Y}_{2}^{2}$ .

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