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Statistics / Mathematical Statistics with Applications 7 / Chapter 7 / Problem 23E

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

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Applet Exercisea Use the applet Chi-Square Probabilities

Chapter 7, Problem 23E

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QUESTION:

Applet Exercise

Use the applet Chi-Square Probabilities and Quantiles to find \(P[Y>E(Y)]\) when Y has \(\mathrm{X}^{2}\) distributions with 10, 40, and 80 df.What did you notice about \(P[Y>E(Y)]\) as the number of degrees of freedom increases as in part (a)?How does what you observed in part (b) relate to the shapes of the \(\mathrm{X}^{2}\) densities that you obtained in Exercise 7.22?

Equation Transcription:

$P[Y>E(Y)]$

${X}^{2}$

$P[Y>E(Y)]$

${X}^{2}$

Text Transcription:

P[Y>E(Y)]

X^2

P[Y>E(Y)]

X^2

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Questions & Answers

QUESTION:

Applet Exercise

Use the applet Chi-Square Probabilities and Quantiles to find \(P[Y>E(Y)]\) when Y has \(\mathrm{X}^{2}\) distributions with 10, 40, and 80 df.What did you notice about \(P[Y>E(Y)]\) as the number of degrees of freedom increases as in part (a)?How does what you observed in part (b) relate to the shapes of the \(\mathrm{X}^{2}\) densities that you obtained in Exercise 7.22?

Equation Transcription:

$P[Y>E(Y)]$

${X}^{2}$

$P[Y>E(Y)]$

${X}^{2}$

Text Transcription:

P[Y>E(Y)]

X^2

P[Y>E(Y)]

X^2

ANSWER:

Step 1 of 5

a)

Let has distribution with degrees of freedom.

Then, and the degrees of freedom,

Consider , then, and the degrees of freedom,

Then,

(Using EXCEL command = chidist )

The applet of the above probability is as follows:

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