Suppose X~Beta(a, B) with X c (0, b]: 1 P(x; a, ß) = - B (a, ß)ba+ß-i **-(b – x)8-1 a) Describe the shape of the probability distribution for the following shape parameters 1. a = B = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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Exercise 6 - Beta Distributions
Suppose X~Beta(a, B) with X c (0, b]:
1
P(x; a, B) :
xa-'(b –
B(a, 8)ba+B-1 **-(b - x)8-1
a) Describe the shape of the probability distribution for the following
shape parameters
1. a = B = 1
2. a = B = 0.25
3. a = B = 3
b) Under which conditions for the shape parameters would the beta
distribution be asymmetric
c) What would distinguish the Kullback-Leibler divergence from the
absolute difference between X-Beta(1,1) and X~Normal(0.5 + b,0)?
Transcribed Image Text:Exercise 6 - Beta Distributions Suppose X~Beta(a, B) with X c (0, b]: 1 P(x; a, B) : xa-'(b – B(a, 8)ba+B-1 **-(b - x)8-1 a) Describe the shape of the probability distribution for the following shape parameters 1. a = B = 1 2. a = B = 0.25 3. a = B = 3 b) Under which conditions for the shape parameters would the beta distribution be asymmetric c) What would distinguish the Kullback-Leibler divergence from the absolute difference between X-Beta(1,1) and X~Normal(0.5 + b,0)?
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