[sthief09]

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Note: f(x,y) must first be normalized by adjusting the constant if necessary such that the double integral of f(x,y) for x from 0 to 1, and y from 0 to 1, is equal to 1.


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a) double integrate f(x,y) for x from 0 to 1, and y from 1-x to 1.


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I got .02 from this. so far, so good I hope

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b) integrate x*f(x,y) for x from 0 to 1.


c) integrate y*f(x,y) for y from 0 to 1.


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when I do this, I am getting 3y/10 and 6/15x^2, respectively. can this be right? can I get rid of the variables from there? the problem is it's a multivariate equation and I'm only integrating for one variable each, so I'm left with one, right?

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d) double integrate xy*f(x,y) for x from 0 to 1, and y from 0 to 1.


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I'm getting 1/10 for this

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e) cov(x,y) = E(xy) - E(x)*E(Y)

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since my answers for E(x) and E(y) have the other variable in them, I'm not going to get a number here. I'm assuming this can't be correct.

I'm going through my book now. you set me on the right path now. at least now I understand what I'm doing. before I was just mindlessly leafing through a book that I already read a couple of years ago