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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Applet Exercise Use the applet Comparison of

Chapter 4, Problem 117E

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QUESTION:

Problem 117E

Applet Exercise Use the applet Comparison of Beta Density Functions to compare beta density functions with (α = 9, β = 7), (α = 10, β = 7), and (α = 12, β = 7).

a Are these densities symmetric? Skewed left? Skewed right?

b What do you observe as the value of α gets closer to 12?

c Graph some more beta densities with α > 1, β > 1, and α > β. What do you conjecture about the shape of beta densities with α > β and both α > 1 andβ > 1?

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QUESTION:

Problem 117E

Applet Exercise Use the applet Comparison of Beta Density Functions to compare beta density functions with (α = 9, β = 7), (α = 10, β = 7), and (α = 12, β = 7).

a Are these densities symmetric? Skewed left? Skewed right?

b What do you observe as the value of α gets closer to 12?

c Graph some more beta densities with α > 1, β > 1, and α > β. What do you conjecture about the shape of beta densities with α > β and both α > 1 andβ > 1?

ANSWER:

Solution:

Step 1 of 4:

  We use the applet comparison of beta density functions to get the Beta density curves for

 and

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