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

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
`(1)/(16)`

1
`^4C_1 (1/2)^(4)` = 1/4
`(5)/(16)`

2
`^4C_2 (1/2)^(4)` = 3/8
`(11)/(16)`

3
`^4C_3 (1/2)^(4)` = 1/4
`(15)/(16)`

4
`^4C_4 (1/2)^(4)` = 1/16 1