# Change of variable

1. Sep 5, 2010

### 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?

Last edited: Sep 6, 2010
2. Sep 6, 2010

### vela

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

3. Sep 6, 2010

### thereddevils

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

4. Sep 6, 2010

### vela

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

5. Sep 6, 2010

### thereddevils

What is the significance of that?

6. Sep 6, 2010

### vela

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

7. Sep 6, 2010

### thereddevils

do i adjust the limit of the integration?

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