Hello

So i have this question: X have the discrete density fX(x) = 1/9 x1 = -1

4/9 x2 = 1/2

4/9 x3= 2

A) What is the discrete density of Y := 1/X ?

my solution: 1/x1 = 1/-1 = -1

1/x2 = 1/(1/2) = 2

1/x3 = 1/2 = 1/2

So basically i get same values from Y = 1/X so discrete density of Y is FY(y) = 1/9 y1 = -1

4/9 y2 = 2

4/9 y3 = 1/2

However, im not sure did i even calculated this right way. Any comments?

Thank you.