Let X1, X2, . . . , Xn denote n independent and

Chapter 9, Problem 37E

(choose chapter or problem)

Let ${X}_{1},{X}_{2},…,{X}_{n}$ denote $n$ independent and identically distributed Bernoulli random variables such that

$P\left(X_{i}=1\right)=p \text { and } P\left(X_{i}=0\right)=1-p$

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 $9.4$ .

Equation Transcription:

${X}_{1},\ {X}_{2},...,{X}_{n}$

$P({X}_{i}=1)=p\ and\ P({X}_{i}=0)=1-p$

$i=1,2,...,n$

${\Sigma{}}_{i=1}^{n}{X}_{i}$

Text Transcription:

X1, X2,...,Xn

P (X_i=1)=p and P (X_i=0)=1-p

i=1,2,...,n

\sum_i=1^n X_i

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