Q95·Section III (Statistics)·95 of 145Given T=tT=tT=t, each XiX_iXi is Bin(t,1/n)\operatorname{Bin}(t,1/n)Bin(t,1/n)Let X1,…,XnX_1,\dots,X_nX1,…,Xn be iid Poisson(λ)(\lambda)(λ). The UMVUE of P[X=x]P[X=x]P[X=x] is (T=∑Xi=tT=\sum X_i=tT=∑Xi=t): OptionsA(tx)(1n)x(n−1n)t−x\binom tx\bigl(\frac1n\bigr)^x\bigl(\frac{n-1}n\bigr)^{t-x}(xt)(n1)x(nn−1)t−x; x=0,1,…,tx=0,1,\dots,tx=0,1,…,tB(tx)(1n)x(n−1n)t−x\binom tx\bigl(\frac1n\bigr)^x\bigl(\frac{n-1}n\bigr)^{t-x}(xt)(n1)x(nn−1)t−x; x=0,1,…,nx=0,1,\dots,nx=0,1,…,nC(tx−1)(1n)x−1(n−1n)t−x+1\binom t{x-1}\bigl(\frac1n\bigr)^{x-1}\bigl(\frac{n-1}n\bigr)^{t-x+1}(x−1t)(n1)x−1(nn−1)t−x+1; x=1,…,nx=1,\dots,nx=1,…,nD(t−1x)(1n)x(n−1n)t−1−x\binom{t-1}x\bigl(\frac1n\bigr)^x\bigl(\frac{n-1}n\bigr)^{t-1-x}(xt−1)(n1)x(nn−1)t−1−x; x=1,…,tx=1,\dots,tx=1,…,tPick an option to check your answer.Show answerShow solution Report a problem with this question← Q94All questionsQ96 →Keyboard: A–D answer · S solution · ←/→ previous/next