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a. The event {X2 y} is equivalent to what event involving

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition | ISBN: 9780495382171 | Authors: Jay L. Devore ISBN: 9780495382171 196

Solution for problem 4.79 Chapter 4

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

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Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition | ISBN: 9780495382171 | Authors: Jay L. Devore

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

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Problem 4.79

a. The event {X2 y} is equivalent to what event involving X itself? b. If X has a standard normal distribution, use part (a) to write the integral that equals P(X2 y). Then differentiate this with respect to y to obtain the pdf of X2 [the square of a N(0, 1) variable]. Finally, show that X2 has a chi-squared distribution with 1 df [see (4.10)]. [Hint: Use the following identity.] d d y b(y) a(y) f(x) dx f[b(y)] b (y) f[a(y)] a (y)

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Chapter 15 Inferences for Regression Chapter 4 was all descriptive statistics (describing the relationship between Y and X in the sample data) and Chapter 15 is inferential statistics (describing the ‘true’ relationship between Y and X in the population) The first few pages of Chapter 15 have two main purposes: o To introduce the population regression model o Briefly review what we did with regression in Chapter 4 The population model is     x . The text does a good job of explaining this model. Y 0 1 The population mean of Y has a linear relation with X. 0 is the population Y-intercept and  1Is the population slope Our sample regression equation statistics (ŷ, b O and b 1 will provide estimates of the p

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Chapter 4, Problem 4.79 is Solved
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Textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online)
Edition: 7
Author: Jay L. Devore
ISBN: 9780495382171

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a. The event {X2 y} is equivalent to what event involving