2
$\begingroup$

Possible Duplicate:
Please correct my answer (Probability)

I have to calculate the density function of the random variable $Y= 1-X^2$, given that: $f(x) = \frac{1}{9}(x+1)^2$, where $-1 < x < 2$.

So I finally understood that the domain of Y is $-3 < Y < 1$.

But it seems that i cant continue further... My method is to find the distribution of Y by using the density function of X , and finally ill find the density function of Y by taking the derivative of Y's distribution func.

Its not working at all, i am taking wrong integral, wrong spaces, everything wrong...

Could someone please explain me what is the correct way?

Thanks

  • 0
    Draw the graph and you see that $Y$ is a non-one-to-one function of $X$, and that's where the difficulty lies, and that's why the thing comes out as a piecewise defined density function.2012-05-24

2 Answers 2