# Thread: Derived Random Variable

1. ## Derived Random Variable

Hi, I am having trouble with one example that is in my text (I have attached it - Example 3.26, the bottom of the pdf is cut off but it just says 0 otherwise)

First, I dont understand why it says, "we first observe that 0 <= Y <= 9". Why is it not 1 <= Y <= 9?

I can't understand either why they go on later to say "For 0 <= y <= 1, -root_y <= x <= root_y"...going on with the next integral as well.

I have been trying to figure out the logic with this question for some time now, but I really feel stuck. Could someone please provide some insight?

Thanks!

2. Originally Posted by scothoward
Hi, I am having trouble with one example that is in my text (I have attached it - Example 3.26, the bottom of the pdf is cut off but it just says 0 otherwise)

First, I dont understand why it says, "we first observe that 0 <= Y <= 9". Why is it not 1 <= Y <= 9? Mr F says: Draw a graph of Y = X^2 over the domain -1 < X < 3. What's the range .......?

I can't understand either why they go on later to say "For 0 <= y <= 1, -root_y <= x <= root_y"...going on with the next integral as well. Mr F says: For those values of y the pdf of X is non-zero. Once y > 1, -sqrt{y} is less than -1 and the pdf of X is zero for those values of x.

I have been trying to figure out the logic with this question for some time now, but I really feel stuck. Could someone please provide some insight?

Thanks!
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