# 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:

Text Transcription:

P[Y>E(Y)]

X^2

P[Y>E(Y)]

X^2

### 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:

Text Transcription:

P[Y>E(Y)]

X^2

P[Y>E(Y)]

X^2

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: