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 boys in each outcome. For example, if the outcome isgbb

,then=

R

gbb

2

.Suppose that the random variableX

is defined in terms ofR

as follows:=

X

R

2

2

R

4

.The values ofX

are given in the table below.Outcomegbb

ggb

bbb

bgg

gbg

ggg

bbg

bgb

Value ofX

4

5

1

5

5

4

4

4

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.

Valuex

ofX

p

X

x