# Pdf of random variable

## Homework Statement

random variable of X has pdf: f(x) = (3/16)*x2 from interval (-2,2). Also, E(X) = 0, and E(X2) = 12/5. Find the pdf of Y = X2

## The Attempt at a Solution

I don't really know where to start.

vela
Staff Emeritus
Homework Helper
There are a couple of methods to do this. One of the easiest to understand conceptually is to calculate the probability that Y is less than or equal to some y in terms of X.

P(Y≤y) = P(X2≤y) = ...

Now P(Y≤y) is just FY(y), the cdf of Y, so to find fY(y), the pdf of Y, just differentiate it.

so first I should find the cdf of X by integrating the pdf of X, then I should find the cdf of Y, and then differentiate that to get the pdf of Y? How do I get the cdf of Y from the cdf of X^2?

vela
Staff Emeritus