If the probability of a boy in a single birth is 1/2 and is independent of the sex of previous babies then the number of boys in a family of 10 children follows a Binomial distribution with mean 5 and variance 2.5. In each of the following instances, describe how the distribution of the number of boys differs from the Binomial described above.

(a) The probability of a boy is 6/10.

(b) The probability of a boy is 1/2 but births are not independent. The birth of a boy makes it more than an even chance that the next child is a boy.

(c) As (b) above, except that the birth of a boy makes it less than an even chance that the next child will be a boy.

(d) The probability of a boy is 6/10 on the first birth. The birth of a boy makes it a more than even chance that the next baby will be a boy.