MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question 2 For the General Beta distribution of the first kind: X bei(a; b; a, ß) when fx(x) Show that E(X) = a + (x-a)-¹(b-x)-1 B(x;ß) (b-a)a+B-1 > a<x<b α αβ (b-a), var(X) = (b-a)² a+ß (a +B)² (a + ß+1) by (i) applying basic principles and (ii) using the fact that X = a + (b-a)Y where Y~ bei(a, ß)
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Transcribed Image Text:Question 2 For the General Beta distribution of the first kind: X bei(a; b; a, ß) when fx(x) Show that E(X) = a + (x-a)-¹(b-x)-1 B(x;ß) (b-a)a+B-1 > a<x<b α αβ (b-a), var(X) = (b-a)² a+ß (a +B)² (a + ß+1) by (i) applying basic principles and (ii) using the fact that X = a + (b-a)Y where Y~ bei(a, ß)
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Step 1: Finding the expected value of x applying basic principle.
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Step 2: Finding the variance of x applying basic principle.
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Step 3: Finding the expected value of x and the variance using the given fact.
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