Can you help me to solve this exercises ?
Using theorems about convergence in probability and continuity at functions, to solve:
Let a random sample from Poisson distribution Xi - Poi (µ)
a)To show that Yn=exp(-X`n) --p--> exp(-µ) = P(X=0) , with X`n = sampler median and --p--> convergence in probability
b)To find the asymptotic normal distribution of Yn=exp(-X`n)
c) To show that X´n exp(-X`n) --p--> µexp(-µ)= P(X=1)
Thank you