Continuous R.V

**matty888** · March 25th 2009, 06:42 AM

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

**Moo** · March 25th 2009, 11:40 AM

Hello,

Originally Posted by matty888

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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