Question

For a family with 4 kids define a random variable X to be equal to the number of boys in the family.

1. Describe and plot probability density and cumulative probability functions.

2. Find the mean and variance of X.

3. Compute and show on the plots the probability of having at least two girls.

Answer 1

1)

n=4

p=0.50

X	P(X)
0	0.0625
1	0.2500
2	0.3750
3	0.2500
4	0.0625

probability density plot

---------------

cumulative probability plot.

2)

Mean = np =    4*0.5=       2.00
Variance = np(1-p) =    4*0.5*(1-0.5)=       1.0000

3)

P(at least 2 girls) = P(at most 2 boy) = P(X≤1) = 0.6875