1. Suppose X1, X2, X- Pois(A), i.e., is a random sample from a Poisson distribution with mean A. The MLE for A is X. (a) How would you construct an exact 95% CI for A based on this MLE? (b) Assuming n is large enough, exploit the CLT and construct an approximate 95% CI for A based on this MLE. (c) How could you study how well the approximate CI works through a simulation study? Write out the steps of the simulation study. You don't need to write any code or use R syntax.

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1. Suppose X1, X2, .,X, ~ Pois(A), i.e., is a random sample from a Poisson distribution
with mean A. The MLE for A is X.
(a) How would you construct an exact 95% CI for A based on this MLE?
(b) Assuming n is large enough, exploit the CLT and construct an approximate 95%
CI for A based on this MLE.
(c) How could you study how well the approximate CI works through a simulation
study? Write out the steps of the simulation study. You don't need to write any
code or use R syntax.
Transcribed Image Text:1. Suppose X1, X2, .,X, ~ Pois(A), i.e., is a random sample from a Poisson distribution with mean A. The MLE for A is X. (a) How would you construct an exact 95% CI for A based on this MLE? (b) Assuming n is large enough, exploit the CLT and construct an approximate 95% CI for A based on this MLE. (c) How could you study how well the approximate CI works through a simulation study? Write out the steps of the simulation study. You don't need to write any code or use R syntax.
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