Question

The random variable x represent the number of boys in a family of three children. Assuming that boys are equally likely, find the mean and standard deviations for the random variable x.

x	Frequency,f	P(x)	x*P(x)	x-μ	(x-μ)2	(x-μ)2*P(x)
Total	N=sum f

Note: *= multiplication

Answer 1

As boys are equally likely.

For three children the possible outcomes are,

BBB=3   
BBG=2   
BGB=2
BGG=1
GBB=2
GBG=1
GGB=1
GGG=0

B represents Boys and G represent Girls

Therefore x takes value {0,1,2,3} from above.

mean (X )

Answer 2

f mode > median > mean, then the distribution is