STAT 4201 Midterm: Statistics 421 Solution_MidI_SP12

• School: Ohio State University
• Department: Statistics
• Course: STAT 4201
• Professor: All

Document Summary

Prof. prem k. goel: [20 points] let x1, x2, . Note that the gamma distribution with = 2 and = /2 is same as the. Chi-square distribution with degrees of freedom, for which e(x) = , and. Therefore the mom estimator m om of is equal to the rst sample moment. 1 e(xi) = e(x), i. e. , x is unbiased for the. X, and its expectation e( x) = pn population mean, if it exists. Hence, m om unbiased estimator for . (b) [4 points] find the variance of the mom estimator. If v ar(x) = 2, it is known that v ar( x) = 2. As mentioned in part (a) above, (c) [10 points] find the maximum likelihood estimator of . Given , the joint density of f (x1, x2, . , xn) is given by f (x1, x2, . Therefore, the log-likelihood function of is given by lnl( ) = nln(2) nln( (