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Compute E(X) and var(X). Hint: If Y ~ beta(a, ß), then E(Y) α a + B and var(Y) = αβ (a + b)²(a +B+1)*

Compute E(X) and var(X). Hint: If Y ~ beta(a, ß), then E(Y) α a + B and var(Y) = αβ (a + b)²(a +B+1)*

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. In a presidential campaign the proportions P of voters who would vote for the democratic candidate over different areas is distributed as beta(a, ß), with PDF f(pla, B) E(Y) = = for 0 < p < 1, a > 0 and ß > 0. Suppose that a total number of n votes are randomly selected from one randomly selected area. Let X denote the number of voters who would vote for the democratic candidate. This leads to the well-known beta-binomial hierarchy: binomial(n, P) beta(a, ß). Compute E(X) and var(X). Hint: If Y ~ beta(a, ß), then r(a)r (3) T(a + B) XP P α a + ß -pa-¹(1 − p)³-1 and var(Y) = ав (a + b)²(a + B + 1)'
Transcribed Image Text:2. In a presidential campaign the proportions P of voters who would vote for the democratic candidate over different areas is distributed as beta(a, ß), with PDF f(pla, B) E(Y) = = for 0 < p < 1, a > 0 and ß > 0. Suppose that a total number of n votes are randomly selected from one randomly selected area. Let X denote the number of voters who would vote for the democratic candidate. This leads to the well-known beta-binomial hierarchy: binomial(n, P) beta(a, ß). Compute E(X) and var(X). Hint: If Y ~ beta(a, ß), then r(a)r (3) T(a + B) XP P α a + ß -pa-¹(1 − p)³-1 and var(Y) = ав (a + b)²(a + B + 1)'
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