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a. The event {X2 # y} is equivalent to what event involvingX itself?b. If X has a

Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore ISBN: 9781305251809 122

Solution for problem 71 Chapter 4.4

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 71

a. The event {X2 # y} is equivalent to what event involvingX itself?b. If X has a standard normal distribution, use part (a)to write the integral that equals P(X2 # y). Then differentiatethis with respect to y to obtain the pdf ofX2 [the square of a N(0, 1) variable]. Finally, showthat X2 has a chi-squared distribution with n 5 1 df[see (4.10)]. [Hint: Use the following identity.]ddy 5#b(y)a(y)f(x) dx6 5 f[b(y)] ? b9(y) 2 f[a(y)] ? a9(y)

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Textbook: Probability and Statistics for Engineering and the Sciences
Edition: 9
Author: Jay L. Devore
ISBN: 9781305251809

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a. The event {X2 # y} is equivalent to what event involvingX itself?b. If X has a