Poisson lambda suppose y has a poisson distribution with

Question

Poisson λ. Suppose Y, has a Poisson distribution with mean Aot,, where the exposure th is known, k = I,.. ., K, and the Y, are statistically independent.

(a) Write the likelihood function for Y,, . . . , Y_λ.

(b) Set the derivative of the log likelihood with respect to h equal to λ zero and solve for the ML estimate λ

c) Calculate the true Fisher information for λ.

 (d) Calculate the true asymptotic variance and standard error of λ.

(e) Give the expression for the large-sample two-sided approximate 1OOy% confidence limits for A, (positive limits).

(f) Calculate such two-sided 95% confidence limits for the yearly failure rate of a power line that had failures over four years.