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 writegbg

,bbb

,etc. For each outcome, letR

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

,then=

R

gbb

1

.Suppose that the random variableX

is defined in terms ofR

as follows:=

X

2

R

2

2

R

3

.The values ofX

are thus:Outcomebgg

ggb

bbb

ggg

bbg

gbb

gbg

bgb

Value of

X

1

1

3

9

3

3

1

3

Calculate the probability distribution function ofX

,i.e. the functionp

X

x

.First, fill in the first row with the values ofX

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

Value

x

of

X

4

3

6

P

X

x

5

2

8