A population consists of m families. Let Xj denote the size of family j, and suppose that X1, . . . ,Xm are independent random variables having the common probability mass function

with mean μ = kkpk. Suppose a member of the population is randomly chosen, in that the selection is equally likely to be any of the members of the population, and let Si be the event that the selected individual is from a family of size i. Argue that

Transcribed Image Text:

p(k) = P(X;=k), Pk = 1 k=1