Solving Change of Variable Homework: Find cdf of Y

[thereddevils]

Homework Statement

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.

Homework Equations

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?