Question

A couple plans to have children until they get a​ girl, but they agree they will not have more than three​ children, even if all are boys. Assume that the probability of having a girl is

0.50.5.

Let X be a random variable indicating how many children the couple will have. Find the standard deviation of the random variable X.

x	11	22	33
​P(X=​x)	0.5000.500	0.2500.250	0.250

Answer 1

Solution :

Mean = = X * P(X)

= 1 * 0.50 + 2 * 0.25 + 3 * 0.25

= 0.50 + 0.50 + 0.75

= 1.75

Standard deviation =

=X ² * P(X) - ²

=  1 * 0.50 + 2² * 0.25 + 3² * 0.25 - 1.75²

= 0.6875

= 0.8292

Standard deviation = 0.8292