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- Dec 14th 2009, 06:24 PM #1

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## P(x<2y)

Pretty simple question:

f(x,y) = {2 if 0 <= x <= y <= 1 , 0 elsewhere}

How do I compute P(X<2Y) ?

Similarly, if I'm given the following CDF,

F(x,y) = (1-exp(-x^2))(1-exp(-y^2)) on {x,y>0}

How would I compute P(X<2Y) here?

Thanks in advance for your help!

- Dec 14th 2009, 06:47 PM #2

- Dec 14th 2009, 07:45 PM #3

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- Dec 15th 2009, 04:23 PM #4
My reply to question 1 is wrong - I misread the support - but my advice remains: Draw a picture and the integral terminals become obvious (provide the question is read properly):

1. .

My reply to question 2 is also wrong - I misread the equation as the**pdf**when it is in fact the**cdf**. You have a number of options for answering the question, including using the given cdf to get the pdf and then integrating the pdf over the region I gave.