Question

Let us assume that the number N of children in a given family follows a Poisson distribution with parameter

. Let us also assume that for each birth, the probability that the child is a girl is p 2 [0; 1], and that the

probability that the child is a boy is q = 1?p. Let us nally assume that the genders of the successive births

are independent from one another.

Let X be the discrete random variable corresponding to the number of girls per family. Give the joint

probability mass function of N and X.

Answer 1

Here we are assuming SN = X1+X2+.......+XN , N represents the no. of births following a poisson distribution say poi() And we have Xi's as iid bernoulli distribution with parameter P(X=1)=probability that a girl is born and P(x=0)= probability that a boy is born .