An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort 

oee

 (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll).

For each outcome, let 

N

 be the random variable counting the number of odd rolls in each outcome. For example, if the outcome is 

oeo

, then 

=Noeo2

. Suppose that the random variable 

X

 is defined in terms of 

N

 as follows: 

=X−2N2−4N1

. The values of 

X

 are given in the table below.

Outcome

eee

ooo

eeo

eoo

ooe

oeo

eoe

oee

Value of 

X

−1

5

−3

−1

−1

−1

−3

−3

Calculate the probabilities 

P=Xx

 of the probability distribution of 

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

P=Xx