An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (

h

) and "tails" (

t

) which we write

hth

,

ttt

,etc.

For each outcome, let

N

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

htt

, then

=Nhtt1

. Suppose that the random variable

X

is defined in terms of

N

as follows:

=XN22N2

. The values of

X

are given in the table below.

Outcome	hht	tth	hhh	htt	hth	thh	tht	ttt
Value of X	2	3	1	3	2	2	3	2

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.