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Math Help - help on to find probability density function!!!

  1. #1
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    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!!
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  2. #2
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    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<k) = \int_{L_1}^{U_1} \int_{L_2}^{U_2} f(x,y) dxdy
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  3. #3
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    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?
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  4. #4
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    Re: help on to find probability density function!!!

    Quote Originally Posted by musademirtas View Post
    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.
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