Exercise5.3 Let Y1, ...,Yn Pois(). InExample2.23,wefoundtheUMVUE p=1(1 1 n )ni =1Yi for p = P(Y 1).

Exercise5.3 Let Y1, ...,Yn ∼Pois(λ). InExample2.23,wefoundtheUMVUEˆ p=1−(1− 1 n )Σni

=1Yi for p = P(Y ≥ 1). Isitconsistent?

vExercise5.4 Let Y1, ...,Yn be arandomsamplewithfinitemean μ and variance σ2. Findtheasymp-

totic distributionsof ¯Y 2 n when μ ̸= 0 and μ = 0, and e−¯Yn .