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!!

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:

$\displaystyle P(I<k) = \int_{L_1}^{U_1} \int_{L_2}^{U_2} f(x,y) dxdy$

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?

Re: help on to find probability density function!!!

Quote:

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.