Question

A couple decides to have 3 children. If none of the 3 is a girl, they will try again; and if they still don’t get a girl, they will try once more. If the random variable X denotes the number of children the couple will have following this scheme, then what is the expected value of X?

Answer 1

Since the couple can have 3 or 4 or 5 children, the space of the random variable X is :

Rx

=

{

3,4,5

}

.

The probability density function of X is given by :

Since the couple can have 3 or 4 or 5 children, the space of the random variable X is Rx={3,4,5}. The probability density function of X is given by :

 

Since the couple can have 3 or 4 or 5 children, the space of the random variable X is :

Rx

=

{

3,4,5

}

.

The probability density function of X is given by :

The Expected Value of X, E(X)\( = \)\( \frac{51}{16} \)