Question

# Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus

triples of "girls" (*g*

) and "boys" (*b*

), which we write *gbg*

, *bbb*

, etc. For each outcome, let *R*

be the random variable counting the number of girls in each outcome. For example, if the outcome is *gbb*

, then =

*R*

*gbb*

1

. Suppose that the random variable *X*

is defined in terms of *R*

as follows: =

*X*

−

2

*R*

2

−

2

*R*

3

. The values of *X*

are thus:Outcome*bgg*

*ggb*

*bbb*

*ggg*

*bbg*

*gbb*

*gbg*

*bgb*

Value of

*X*

1

1

−

3

9

−

3

−

3

1

−

3

Calculate the probability distribution function of *X*

, i.e. the function *p*

*X*

*x*

. First, fill in the first row with the values of *X*

. Then fill in the appropriate probabilities in the second row.

Value

*x*

of

*X*

4

3

6

*P*

*X*

*x*

−

5

2

8