Question

2) A couple plans to have 5 children. Let the random variable, x, be the number of girls that will occur. Assume that a boy or a girl is equally likely to occur and that the sex of any successive child is unaffected by the previous brothers or sisters.

a) Enter the probabilities in a table if the random variable, x, can take on values 0, 1, 2, 3, 4, and 5.

b) Find the mean number of girls (expected value) that will occur among the 5 births.

c) Find the variance for the number of girls that will occur.

Answer 1

here this is binomial with parameter n=5 and p=0.5

a)

x	P(x)
0	0.03125
1	0.15625
2	0.3125
3	0.3125
4	0.15625
5	0.03125

b)

mean E(x)=μ=np=5*0.5 =2.5

c)

Var(x) =σ2=(np(1-p))=5*0.5*(1-0.50)=1.25