# 230hw3 - December 18, 2009 MATH 230 Homework #3 (Due:...

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December 18, 2009 MATH 230 Homework #3 (Due: December 29, Tuesday) {Please, submit your homework to my office (SA105) by 17:30 p.m.} 1. Show that the sample variance, S 2 is an unbiased estimator for population variance σ 2 . 2. If Y has a binomial distribution with parameters n and p a) Show that Y/n is an unbiased estimator of p. b) To estimate the variance of Y , we generally use n(Y/n)(1-Y/n) . Show that this estimator is a biased estimator of Var(Y). c) Modify n(Y/n)(1-Y/n) to form an unbiased estimator of Var(Y). 3. The interarrival times (in minutes) at a certain checkout counter during a weekday is uniformly distributed over the interval ( 0, θ ), where θ is unknown interarrival time. Suppose n X X X , , , 2 1 denote a random sample of interarrival times, a) Find an unbiased estimator, θ ˆ of that makes use of the entire sample. b) Find variance of ˆ . 4. The lifetimes of a component are assumed to be exponential with parameter β. 10 of these components were placed on test independently. The only data

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## This note was uploaded on 12/22/2011 for the course CS 101 taught by Professor Dat during the Spring '11 term at Bilkent University.

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230hw3 - December 18, 2009 MATH 230 Homework #3 (Due:...

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