Alright, in this one, I'm given X~U(-1, 3) -1<x<3
Y = X²
Ok, so I know that the domain of y should be 0 < y< 9...right?
Oh, and the pdf(x) = 1/4, -1 < x< 3
So I said, F(y) = P(Y <= y) = P(X² <= y) = P(X <= (y)^1/2
I integrated from (y)^1/2 to 3, dx/4 which gave me, F(y) = 3-(y)^1/2 / 4
So to get the pdf(y), I took the derivative, giving me 1/8*y^1/2
My question is...how do I know the domain for this f(y). Is it for the whole 0<y<9? Or just part? If just part of it, how do I get the other f(y).
Next question is how do I find the Cox(X,Y) over a continuous function? I know how to get marginal and mean, but not covariance.
Then my last questions reads:
Let X and Y have the joint pmf defined by f(0,0) = f(1,2) = 0.2
f(0,1) = f(1,1) = 0.3
Depict the points and probabilities on a graph, giving the marginalpmf's in the margins.
Can someone show me what the graph would look like? I know of course where the points go, but I'm not sure what they mean about the marginal pmf in the margins.