Question

(a) Let \underline{X} = (X_1, ..., X_n) be iid Bin(1, p) random sample. Check if $T(\underline{X}) = \sum_{i=1}^{n} X_i$ is sufficient for p.

Name: (a) Let X = (X1, ..., Xn) be iid Bin(1, p) random sample. Check if T(X) = ∑i=1^n Xi is sufficient for p.
Uploaded: 2023-06-26T07:51:50-08:00
Duration: 6 min 59 s
Channel: Madhur L
Description: (a) Let X = (X1, ..., Xn) be iid Bin(1, p) random sample. Check if T(X) = ∑i=1^n Xi is sufficient for p.

          (a) Let \underline{X} = (X_1, ..., X_n) be iid Bin(1, p) random sample. Check if $T(\underline{X}) = \sum_{i=1}^{n} X_i$ is sufficient for p.

Added by Jose A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

06/26/2023

Step 1

.., Xn. Since they are iid Binomial random variables with parameters 1, p, the joint pmf is given by: f(x1, x2, ..., xn; p) = p^Σxi * (1-p)^(n-Σxi) Show more…

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Use Sufficiency definition (conditional joint pdf/pmf) to solve it. Do not use Factorization theorem. Solve it clearly and in detail. Parameter or not: Let X1, X2, ..., Xn be iid Binomial random variables with parameters 1, p. Check if T = X1 + X2 + ... + Xn is sufficient for p.