Question

Suppose that a couple in planning 3 children is primarily interested in the number of boys.

1) - Define the random variable X.

2) - What is the range of X?

3) - Find the probability function of X.

4) - Find the probability mass function

5) - Draw the graph for the probability mass function

Answer 1

1) Let random variable X be  number of boys.

2)

$$S=\{BBB, BBG, BGB, GBB,$$

$$BGG,GBG, BGG, GGG\}$$

$$Range(X)=\{0,1,2,3\}$$

3)

$$P(X=0)=\dfrac{1}{8}$$

$$P(X=1)=\dfrac{3}{8}$$

$$P(X=2)=\dfrac{3}{8}$$

$$P(X=3)=\dfrac{1}{8}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 & 3 \\ \hline p(x) & 1/8 & 3/8 & 3/8 & 1/8 \\ \end{array}$$

4)

$$f(x) = \begin{cases} 1/8, &x=0 \\ 3/8, &x=1 \\ 3/8, &x=2 \\ 1/8, &x=3 \\ \end{cases}$$

5)