a If Y 3X2 find the probability mass function of Y 12 14 18

a. If Y = (3-X)² find the probability mass function of Y

Solution

If

Y = (3-x)^2, then

x   y
1   4
2   1
3   0
4   1

Thus, we add up P(y = 1) = P(x =2) + P(x = 4).

Therefore,

pdf(y) = 1/2 , y = 4
3/8 , y = 1
1/8 , y = 0
0, otherwise [ANSWER]