**Problem 9.37**Let \( X_1, X_2, \ldots, X_n \) denote \( n \) independent and identically distributed Bernoulli random variables such that\[ P(X_i = 1) = p \quad \text{and} \quad P(X_i = 0) = 1 - p, \]for each \( i = 1, 2, \ldots, n \). Show that \( \sum_{i=1}^{n} X_i \) is sufficient for \( p \) by using the factorization criterion given in Theorem 9.4.

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Answered: 9.37 Let X₁, X2,..., X, denote n…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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9.37 Let X₁, X2,..., X, denote n independent and identically distributed Bernoulli random vari- ables such that P(X; = 1) = p and P(X; = 0) = 1- p, =1 for each i = 1, 2, ..., n. Show that ΣX; is sufficient for p by using the factorization criterion given in Theorem 9.4.