change of variable

[thereddevils]

1. The problem statement, all variables and given/known data

Let X be a random variable with pdf f(x)=2x , for 0<x<1 and let Y=X^2, find the cdf of Y.

2. Relevant equations



3. The attempt at a solution

cdf = P(Y<=y) = P(X^2<=y)

= P(-\sqrt{y}\leq X\leq \sqrt{y})

=\int^{\sqrt{y}}_{-\sqrt{y}}2x dx

= 0 for 0<y<1

Am i correct?

[vela]

You're close. Remember that f(x) is non-zero only on the interval [0,1].

[thereddevils]

You're close. Remember that f(x) is non-zero only on the interval [0,1].

Thanks Vela, but why did i get 0 for the interval [0,1]

[vela]

Again: f(x) is non-zero only on the interval [0,1].

[thereddevils]

Again: f(x) is non-zero only on the interval [0,1].

What is the significance of that?

[vela]

Check your limits of integration, keeping in mind my previous posts.

[thereddevils]

Check your limits of integration, keeping in mind my previous posts.

do i adjust the limit of the integration?