Applet Exercise Refer to Exercise 4.113. Use the applet

Chapter 4, Problem 114E

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QUESTION:

Applet Exercise Refer to Exercise 4.113. Use the applet Comparison of Beta Density Functions to compare beta density functions with \((\alpha=1, \beta=1)\), \((\alpha=1, \beta=2)\) and \((\alpha=2, \beta=1)\).
a What have we previously called the beta distribution with \((\alpha=1, \beta=1)\)?
b Which of these beta densities is symmetric?
c Which of these beta densities is skewed right?
d Which of these beta densities is skewed left?
*e In Chapter 6 we will see that if  is beta distributed with parameters \(\alpha\) and \(\beta\), then \(Y^{*}=1-Y\) has a beta distribution with parameters \(\alpha^{*}=\beta\) and \(\beta^{*}=\alpha\). Does this explain the differences in the graphs of the beta densities?

Equation Transcription:

Text Transcription:

(alpha=1,beta=1)

(alpha=1,beta=2)

(alpha=2,beta=1)

(alpha=1,beta=1)

alpha

beta

Y*=1-Y

alpha*=beta

beta*=alpha

Questions & Answers

QUESTION:

Applet Exercise Refer to Exercise 4.113. Use the applet Comparison of Beta Density Functions to compare beta density functions with \((\alpha=1, \beta=1)\), \((\alpha=1, \beta=2)\) and \((\alpha=2, \beta=1)\).
a What have we previously called the beta distribution with \((\alpha=1, \beta=1)\)?
b Which of these beta densities is symmetric?
c Which of these beta densities is skewed right?
d Which of these beta densities is skewed left?
*e In Chapter 6 we will see that if  is beta distributed with parameters \(\alpha\) and \(\beta\), then \(Y^{*}=1-Y\) has a beta distribution with parameters \(\alpha^{*}=\beta\) and \(\beta^{*}=\alpha\). Does this explain the differences in the graphs of the beta densities?

Equation Transcription:

Text Transcription:

(alpha=1,beta=1)

(alpha=1,beta=2)

(alpha=2,beta=1)

(alpha=1,beta=1)

alpha

beta

Y*=1-Y

alpha*=beta

beta*=alpha

ANSWER:

Solution:

Step 1 of 5:

We have to use the applet comparison of Beta density function to compare density function with (), (), and ()

a)

      The claim is to check for Beta density function to compare density function with ()

From the applet

From the above figure we can see that, when () the Beta distribution is a Uniform distribution,


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