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Unformatted text preview: X 1 ,X 2 ,...,X n following N ( , 2 ) with known but 2 unknown. In this case, n i =1 ( X i- ) 2 / 2 is a valid pivot and can be used to nd a condence interval for 2 . (2 5 = 10 points). (2) Consider the model Y i = X i + i for i = 1 , 2 ,...,n . Here the X i s are xed constants and the s are i.i.d N (0 , 2 ) random variables. (a) Are the Y i s independent and identically distributed in this case? Explain. (b) Find the M.L.Es of ( , ) ( 7 points). (3) Let X 1 and X 2 be two i.i.d. observations from an Exponential( ) distribution. Suppose X 1 = 1 . 8 and X 2 = 2 . 6. Find a condence interval for based on the above data. (6 points) Note: Tables of quantiles of standard distributions are available in the Appendix Section of Rices book. 1...
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This note was uploaded on 04/14/2010 for the course STATS 426 taught by Professor Moulib during the Winter '08 term at University of Michigan.
- Winter '08