Suppose that the genders of the three children of a certain family are soon to be revealed.Outcomesare thus triples of "girls"(g

)and "boys"(b

),which we writegbg

,bbb

,etc. For each outcome, letR

be therandom variablecounting the number of girls in each outcome. For example, if the outcome isbbg

,then=

R

bbg

1

.Suppose that the random variableX

is defined in terms ofR

as follows:=

X

R

4

.The values ofX

are given in the table below.Outcomebgb

ggb

bbb

bgg

ggg

gbb

gbg

bbg

Value ofX

3

2

4

2

1

3

2

3

Calculate the values of theprobability distributionfunction ofX

,i.e. thefunctionp

X

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

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