- #1
whitejac
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Homework Statement
E = { (x,y) | |x| + |y| ≤ 1}
fx,y (x,y) =
{
c (x,y) ∈ E
0 otherwise
}
Find C.
Find the Marginal PDFs
Find the conditional X given Y=y, where -1 ≤ y ≤ 1.
Are X and Y independent.
Homework Equations
I'm taking a guess here in the solution...
but F(x,y) = F(x)F(y)
and f(x,y) = f(x)f(y)
These will be used later, when I'm wishing to find the Marginals and the independence.
The Attempt at a Solution
So, this is a uniform distribution (if it's not stated in my pdf, it's stated in the problem's text.)
Considering that this an "area" I should just be able to integrate this with respect to the bondaries correct?
That would be ∫0,1∫00,1cdxdy? Then c = 1, or do I base it off of E? Then it should be bounded from [-1,1]?
This is what I believe it to be, but I'm not entirely sure. My professor gave a solution that was probably more general where he found something else first, but i didn't quite get it because he was trying to rush it at the end of class.
After finding C, the marginals are the integrals with respect to y and x to give us the "trace" of the density function.