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Statistics / Probability and Statistical Inference 9 / Chapter 5.4 / Problem 5E

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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Let Z1,Z2, . . . ,Z7 be a random sample from the standard

Chapter 5, Problem 5E

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QUESTION:

Let \(Z_{1}, Z_{2}, \ldots, Z_{7}\) be a random sample from the standard normal distribution \(N(0,1)\). Let \(W=Z_{1}^{2}+Z_{2}^{2}+\) \(\cdots+Z_{7}^{2}\). Find \(P(1.69<W<14.07)\).

Equation Transcription:

${Z}_{1},{Z}_{2},…,{Z}_{7}$

$N(0,1)$

$W={Z}_{1}^{2}+{Z}_{2}^{2}+$ $\cdots{}+{Z}_{7}^{2}$

$P(1.69<W<14.07)$

Text Transcription:

Z_1,Z_2,…,Z_7

N(0,1)

W=Z_1^2+Z_2^2+ +Z_7^2

P(1.69<W<14.07)

Questions & Answers

QUESTION:

Let \(Z_{1}, Z_{2}, \ldots, Z_{7}\) be a random sample from the standard normal distribution \(N(0,1)\). Let \(W=Z_{1}^{2}+Z_{2}^{2}+\) \(\cdots+Z_{7}^{2}\). Find \(P(1.69<W<14.07)\).

Equation Transcription:

${Z}_{1},{Z}_{2},…,{Z}_{7}$

$N(0,1)$

$W={Z}_{1}^{2}+{Z}_{2}^{2}+$ $\cdots{}+{Z}_{7}^{2}$

$P(1.69<W<14.07)$

Text Transcription:

Z_1,Z_2,…,Z_7

N(0,1)

W=Z_1^2+Z_2^2+ +Z_7^2

P(1.69<W<14.07)

ANSWER:

Problem 5E

Let be random variable from the standard normal distribution . Let . Find

Step by Step Solution

Step 1 of 2

It is known that for random variable having standard normal distribution , if these random variables are independent, then has a distribution that is

Accordingly, let be random variable from the standard normal distribution. Let .

Here, n=7. Therefore, has a distribution that is

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