Paran,k∈\N conk≤n,\[ \P(M = k \mid M + N = n) = \frac{\P(M = k, M + N = n)}{\P(M + N = n)} = \frac{\P(M = k, N = n - k)}{\P(N + M = n)} = \frac{\P(M = k) \P(N = n - k)}{\P(M + ...Paran,k∈\N conk≤n,\P(M=k∣M+N=n)=\P(M=k,M+N=n)\P(M+N=n)=\P(M=k,N=n−k)\P(N+M=n)=\P(M=k)\P(N=n−k)\P(M+N=n) Subsitituting en los PDF de Poisson da\P(M=k∣M+N=n)=(e−aak/k!)(e−bbn−k/(n−k)!)e−(a+b)(a+b)n/n!=n!k!(n−k)!(aa+b)k(1−aa+b)n−k
