What are "x1", "x2", and "x3"? Don't you just mean fX(x)= 1/9 if x= -1, fX(x)= 4/9 if x=1/2, and fX(x)= 4/9 if x= 2 (which is the same as saying fX(-1)= 1/9, fX(1/2)= 4/9, and fX(2)= 4/9)?

Yes, that is correct (although I still don't like your use of "y1", "y2", "y3" instead of just y= -1, y= 2, y= 1/2).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.