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Math Help - Continuous R.V

  1. #1
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    Continuous R.V

    If X and Y are continuous random variables with joint probability density function



    a) Calculate P[2X^2 <Y]

    b)

    Any help would be appreciated
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    Hello,
    Quote Originally Posted by matty888 View Post
    If X and Y are continuous random variables with joint probability density function



    a) Calculate P[2X^2 <Y]
    P(2X^2<Y)=\mathbb{E}\left(\bold{1}_{Y>2X^2}\right)  =\int_0^1 \int_0^1 f_{X,Y}(x,y) \bold{1}_{y>2x^2} ~dy ~dx
    =\int_0^1 \int_{2x^2}^1 (x+y) ~dy ~dx
    Can you calculate this ?
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