# Thread: help on to find probability density function!!!

1. ## help on to find probability density function!!!

hey guys, i am really confused on something.here is the thing:
i have;

i=x+(x^2-y)^(1/2)

and here x is uniform distribution on (a,b)
y is uniform distribution on (c,d)
x and y independent
and there is no information about a,b,c,d.but if you need you can assume anything like a>c.
i need to find the probability density function of i but how??????
actually i dont know how to start!!

2. ## Re: help on to find probability density function!!!

You are going to try and calculate P(I < k), for any value k.

So you need to find the combinations of x,y which gives I<k.

Solve the inequality $\displaystyle x + \sqrt{(x^2 - y)} < k$

Then use your results to set the limit in the integral:
$\displaystyle P(I<k) = \int_{L_1}^{U_1} \int_{L_2}^{U_2} f(x,y) dxdy$

3. ## Re: help on to find probability density function!!!

hi springfan25
thanks for the help but i couldnt do it.i used your help to solve it but i didnt get any solution.can you solve it?

4. ## Re: help on to find probability density function!!!

Originally Posted by musademirtas
hi springfan25
thanks for the help but i couldnt do it.i used your help to solve it but i didnt get any solution.can you solve it?
Please show all your working.