This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: STA 4322/5328 – Spr/2010 Major Exam1 PRINT NAME _____________ For all problems, the sample mean, sample variance, and sample proportion are: ( 29 ) , ( ~ where : Proportion Sample 1 1 : variance Sample 1 : Mean Sample ^ 1 2 1 p n Bin Y n Y p Y Y n Y n Y n i i n i i = = ∑ ∑ = = Q.1: Suppose Y 1,…, Y n denote a random sample from a population with an exponential distribution whose density is given by (where Y~Exp ( θ )): ( 29 2 / ) ( ) ( then ) ( ~ If : Note elsewhere , 1 ) ( θ θ θ θ θ θ = = = Y V Y E Exp Y y e y f y If Y (1) = min( Y 1,…, Y n ) then density function for Y (1) is: ( 29 ( 29 ( 29 = = elsewhere , * / 1 1 * / / 1 ) 1 ( 1 1 θ θ θ θ θ y e e n y g y ny P.1.a. Give the mean and variance of Y (1) ANSWER: ( 29 ( 29 ( 29 2 2 ) 1 ( ) 1 ( * * = = = = n Y V n Y E θ θ θ θ P.1.b. Give a function of Y (1) that is an unbiased estimate of θ : ( 29 ) 1 ( 1 ^ Y h = θ ANSWER: ) 1 ( 1 ^ nY = θ P.1.c. Give the variance of your estimator in Part P.1.b. ANSWER: ( 29 ( 29 2 2 2 2 ) 1 ( 2 ) 1 ( 1 ^ θ θ θ = = = = n n Y V n nY V V P.1.d. Give the variance of the unbiased estimator Y = 2 ^ θ ANSWER: n n Y V V 2 2 ^ ) ( θ θ = = Q.2: An engineer is interested in estimating the mean breaking strength of a new material to be used in satellites. Because the material is so expensive, she can only obtain n = 9 test measurements. She obtains a sample mean of 3000 psi and a sample standard deviation of 300 psi. sample mean of 3000 psi and a sample standard deviation of 300 psi....
View
Full
Document
This note was uploaded on 03/11/2011 for the course STA 4322 taught by Professor Winner during the Spring '10 term at West Chester.
 Spring '10
 Winner
 Statistics, Variance

Click to edit the document details