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Applet Exercise Use the applet Comparison of
Chapter 4, Problem 119E(choose chapter or problem)
Problem 119E
Applet Exercise Use the applet Comparison of Beta Density Functions to compare beta density functions with (α = 4, β = 0.3), (α = 7, β = 0.3), and (α = 12, β = 0.3).
a Are these densities symmetric? Skewed left? Skewed right?
b What do you observe as the value of α gets closer to 12?
c Which of these beta distributions gives the highest probability of observing a value less than 0.8?
d Graph some more beta densities withα > 1 andβ < 1. What do you conjecture about the shape of beta densities with α > 1 andβ < 1?
Questions & Answers
QUESTION:
Problem 119E
Applet Exercise Use the applet Comparison of Beta Density Functions to compare beta density functions with (α = 4, β = 0.3), (α = 7, β = 0.3), and (α = 12, β = 0.3).
a Are these densities symmetric? Skewed left? Skewed right?
b What do you observe as the value of α gets closer to 12?
c Which of these beta distributions gives the highest probability of observing a value less than 0.8?
d Graph some more beta densities withα > 1 andβ < 1. What do you conjecture about the shape of beta densities with α > 1 andβ < 1?
ANSWER:
Answer:
Step 1 of 4:
(a)
Applet Exercise Use the applet Comparison of Beta Density Functions to compare beta density functions with
We need to find the symmetry of these densities whether it is Skewed left or Skewed right.
Figure 1: Comparison of beta density functions with the different values of
From the figure 1, we can see that all the densities are positive and left skewed because the highest points lie to the right of the graph..
Hence all of the densities with the different value of are Skewed left.