Question

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, BBBB, BBBB, BBBB, BBBB, etc.) are equally probable.

Answer 1

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             $^4C_0 (1/2)^{4}$        = 1/16                     $\frac{1}{16}$

1               $^4C_1 (1/2)^{4}$       = 1/4                       $\frac{5}{16}$

2                $^4C_2 (1/2)^{4}$      = 3/8                      $\frac{11}{16}$

3                $^4C_3 (1/2)^{4}$      = 1/4                       $\frac{15}{16}$

4                  $^4C_4 (1/2)^{4}$    = 1/16                      1