Q2.Let X1,…Xn be independent and identically distributed discrete random variables with

Q2.Let X1,…Xn be independent and identically distributed discrete random variables withPoisson(A)distribution:P(X:=x;A)=e-AandE(Xa)=入，fori=1,..,n,入>0，andx=0,1,2,..(a)Find a sufficient statistic for入.[3](b)The following estimator,0,is proposed as an estimator for 0=g(A)=e-1if X=0;0otherwise.Show that 0 is an unbiased estimator of 0.[5](c)Calculate E[|T=t,where T=∑n1Xi.[7](d)Find a Minimum Variance Unbiased Estimator (MVUE)of 0.Discuss if this is aunique estimator.[10]Hint:You can use that if X1,…Xm are independent and identically distributed dis-crete random variables with Poisson(A)distribution,then∑n1Xi~Poisson(mA).