Then f(n;ξ，)=k(n){P(=0)}oΠ空1{P(=)}” -)a" =o+-6{-2之e(剑)] where k(n)=>o1ni/no!n!...ne!.Obviously,the complete-data sufficient statistic is (nA,nB,n1,n2,...,n6).The complete-data log-likelihood is (5,n)=nol1og(ξ+(1-)e-A) +(N-no)log(1-)-+∑in log入+const. i=l Thus,the complete-data log-likelihood is linear in the sufficient statistic.The E-step requires the computing of Es.(n nobs). This computation results in Es.(ni nobs)=ni for i=1,...,6, and noξ Ec(nAb）=E+(1-S)exp(-万' since na is Binomial(no,p)with p where pA-and pB =(1-E)e-.The expression for Es(nBlnobs)is equivalent to that for E(nA)and will not be needed for E- step computations.So the E-step consists of computing noE(t) n9=9+1-)exp-(可 (1) at the tth iteration. For the M-step,the complete-data maximum likelihood estimate of (A)is needed. To obtain these,note that na Bin(N,E)and that nB,n,...,n6 are observed counts for i=0,1,...,6 of a Poisson distribution with parameter A.Thus,the complete-data maximum likelihood estimate'sofξand入are 7Then f(n; ξ, λ) = k(n) {P(y0 = 0)} n0 Π ∞ i=1 {P(yi = i)} ni = k(n) h ξ + (1 − ξ) e −λ in0 " Π 6 i=1 ( (1 − ξ) e −λλ i i! )ni # = k(n) h ξ + (1 − ξ)e −λ inA+nB n (1 − ξ)e −λ oP6 i=1 ni " Π 6 i=1 λ i i! !ni # . where k(n) = P6 i=1 ni/n0!n1! . . . n6!. Obviously, the complete-data sufficient statistic is (nA, nB, n1, n2, . . . , n6). The complete-data log-likelihood is `(ξ, λ; n) = n0 log(ξ + (1 − ξ)e −λ ) + (N − n0)[log(1 − ξ) − λ] + X 6 i=1 i ni log λ + const. Thus, the complete-data log-likelihood is linear in the sufficient statistic. The E-step requires the computing of Eξ,λ(n|nobs). This computation results in Eξ,λ(ni |nobs) = ni for i = 1, ..., 6, and Eξ,λ(nA|nobs) = n0ξ ξ + (1 − ξ) exp(−λ) , since nA is Binomial(n0, p) with p = pA pA+pB where pA = ξ and pB = (1 − ξ) e −λ . The expression for Eξ,λ(nB|nobs) is equivalent to that for E(nA) and will not be needed for E￾step computations. So the E-step consists of computing n (t) A = n0ξ (t) ξ (t) + (1 − ξ (t) ) exp(−λ (t) ) (1) at the t th iteration. For the M-step, the complete-data maximum likelihood estimate of (ξ, λ) is needed. To obtain these, note that nA ∼ Bin(N, ξ) and that nB, n1, . . . , n6 are observed counts for i = 0, 1, . . . , 6 of a Poisson distribution with parameter λ. Thus, the complete-data maximum likelihood estimate’s of ξ and λ are ˆξ = nA N , 7