STAT 4201 Midterm: STAT 421 OSU Solution MidII SP12

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

Document Summary

Stat 421, spring 2012: [20 points] suppose that a random sample x1, x2, . The pdf of n (0, 2), from appendix c, is i=1 x2 i . n pn f (xi; 2) = Taking the natural log on both sides, the log-likelihood function is given by lnl = n. Taking the derivative of lnl with respect to 2, and setting it equal to 0, we get n. The unique solution of this equation, i. e. , the mle of 2 under the whole param- eter space , is given by. We will use this mle in the next problem. Remark: this problem is exactly same as exercise 10. 62 with = 0, which was an assigned problem in homework 3. (b) [6 points] show that the likelihood ratio test statistic can be expressed as: We rst obtain simpli ed expressions for the numerator and the denomiantor of the likelihood ratio statistic .