Solution Found!
Applet Exercise Refer to Exercise 4.113. Use the applet
Chapter 4, Problem 114E(choose chapter or problem)
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,