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STAT 801

Problems: Assignment 6

  1. Suppose tex2html_wrap_inline15 are independent Poisson( tex2html_wrap_inline17 ) variables. Find the UMP level tex2html_wrap_inline19 test of tex2html_wrap_inline21 versus tex2html_wrap_inline23 and evaluate the constants for the case n=3 and tex2html_wrap_inline27 .
  2. Suppose X has a Gamma( tex2html_wrap_inline31 ) distribution with shape parameter tex2html_wrap_inline33 known. Find the UMPU test of tex2html_wrap_inline35 and evaluate the constants for the case tex2html_wrap_inline37 and tex2html_wrap_inline39 .
  3. Suppose tex2html_wrap_inline41 are iid exponential( tex2html_wrap_inline43 ).

    1. Find the exact confidence levels of 95% intervals based on normal approximations to the distributions of the pivots tex2html_wrap_inline45 , tex2html_wrap_inline47 , and tex2html_wrap_inline49 for n=10, 20 and 40.
    2. Find the shortest exact 95% confidence interval based on tex2html_wrap_inline53 ; get numerical values for n=10, 20 and 40.
    3. Find the exact confidence level of 95% confidence intervals based on the chi-squared approximation to the distribution of deviance drop. Compare the results with the previous question based on length and coverage probabilities. Figure out how to make a convincing comparison. Which method is better?

  4. Page 398. Q 1.
  5. Page 398 Q 2.
  6. Page 398. Q 6.



Richard Lockhart
Tue Apr 15 22:46:17 PDT 1997