help on to find probability density function!!!

• Jun 29th 2011, 07:03 PM
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!!
• Jun 30th 2011, 04:07 AM
SpringFan25
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 $x + \sqrt{(x^2 - y)} < k$

Then use your results to set the limit in the integral:
$P(I
• Jul 2nd 2011, 09:52 PM