From families with four children a family is chosen at random. Let X be the number of boys in the family. Calculate and sketch the distribution function of X. Assume that in a four-child family all gender distributions (for example, , , , , etc.) are equally probable.

Solution :

Given :

X = the number of boys in a family of four children

Families having four children are chosen randomly.

The gender distribution in the four child family are equally probable.

Thus,

 X                P(X)                                          CDF

0                    = 1/16                    

1                     = 1/4                      

2                      = 3/8                      

3                      = 1/4                      

4                      = 1/16                      1

-6 is the correct option from the above given options