6. Suppose that you observe three independent Poisson observations Y1: Y, Y3 with means λ,A2,A3 respectively....
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE of λ based on (Yi,Yo) (b) Show that the estimator λ (Y + Y)/3 is unbiased for λ and compute its variance. (c) With as much rigor as possible, show that if A is large then (A-X)/v is approximately normally distributed. (d) Derive a 95 percent confidence interval for A based on the asymptotic distribution of λ in part (c) (e) Extra Credit Based on part...