Exercise 6 - Beta DistributionsSuppose X~Beta(a, B) with X c (0, b]:1P(x; a, B) :xa-'(b –B(a, 8)ba+B-1 **-(b - x)8-1a) Describe the shape of the probability distribution for the followingshape parameters1. a = B = 12. a = B = 0.253. a = B = 3b) Under which conditions for the shape parameters would the betadistribution be asymmetricc) What would distinguish the Kullback-Leibler divergence from theabsolute difference between X-Beta(1,1) and X~Normal(0.5 + b,0)?

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Description: Exercise 6 - Beta DistributionsSuppose X~Beta(a, B) with X c (0, b]:1P(x; a, B) :xa-'(b –B(a, 8)ba+B-1 **-(b - x)8-1a) Describe the shape of the probability distribution for the followingshape parameters1. a = B = 12. a = B = 0.253. a = B = 3b) Unde

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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

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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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)?

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