) Show that if is an unbiased estimator of 0 and Var(6) + 0, then n² is not an unbiased estimator of 0². ) Let X be a binomial random variable with parameters n and p. (i) Show that the sample proportion P = X is an unbiased estimator of p. (ii) Determine whether X X 1 is an unbiased estimator of the variance of X.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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(a) Show that if ô is an unbiased estimator of 0 and Var(ê) + 0, then ôn² is not an unbiased
estimator of 0².
(b) Let X be a binomial random variable with parameters n and p.
X
(i) Show that the sample proportion P = – is an unbiased estimator of p.
(ii) Determine whether
X
- -
n
is an unbiased estimator of the variance of X.
Transcribed Image Text:Question (a) Show that if ô is an unbiased estimator of 0 and Var(ê) + 0, then ôn² is not an unbiased estimator of 0². (b) Let X be a binomial random variable with parameters n and p. X (i) Show that the sample proportion P = – is an unbiased estimator of p. (ii) Determine whether X - - n is an unbiased estimator of the variance of X.
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