Estimation (ISS Statistics Paper II (Old Subjective Pattern)): Questions 13 - 14 of 14

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Question number: 13

» Estimation » Optimal Properties » Minimum Variance Bound Estimators

Appeared in Year: 2015

Essay Question▾

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Let X 1, X 2, …, X n be a random sample from the probability distribution with density

fX(x,θ)=1θexθ;0<x<

= 0; otherwise

where 0 < θ < ∞. Show that X=1ni=1nXi is a minimum variance bound estimator and has variance θ2n .

Explanation

By using Cramer-Rao lower bound we find the minimum variance

fX(x,θ)=1θexθ

logfX(x,θ)=logθxθ

θlogfX(x,θ)… (191 more words) …

Question number: 14

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X 1, X 2, … X n be a random sample from the binomial distribution with probability mass function

f(x,θ)={θx(1θ)1x;x=0, 1;0<θ<10;otherwise

Examine whether the statistic T=i=1nXi is complete for this distribution.

Explanation

We know that T=i=1nXi is sufficient statistic for this distribution. Then,

f(x_,θ)=θi=1nxi(1θ)ni=1nxi

p… (226 more words) …

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