- #1

CivilSigma

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## Homework Statement

For

$$f_x(x)=4x^3 ; 0 \leq x \leq 1$$

Find the PDF for $$ Y < y=x^2$$

## The Attempt at a Solution

So, we take the domain on x to be:

$$0\leq x \leq \sqrt y$$

and integrate:

$$ \int_0^{\sqrt y} f_x(x) dx = \int_0^{\sqrt y} 4x^3 dx$$

Do we integrate with respect to x or y? I am not sure about this part of the problem.

If we solve the integral above we get:

$$f_x(y)=y^2 ; y \leq x^2 $$

Is this approach correct?

Thank you.