Finding Marginal Pdf's for a Joint PDF

[hoddo]

Joint PDF --> Marginal Pdf's

Homework Statement

Suppose that the random vector (X, Y ) has the probability density function
(pdf)
fX,Y (x, y) = k(x − y), if 0 < y < x < 1
0, otherwise.
1. Find the value of k, so that fX,Y (x, y) is a genuine pdf.
2. Find the marginal density function of Y , fY (y) and of X, fX(x).

Homework Equations

The Attempt at a Solution

1. k = -6 (using 0<y<x, 0<x<1)
2. fY(y) ?
fX(x) = 3x^2

...having trouble finding fY(y) that eventuates at a true pdf?

 

[haruspex]

k = -6

How can it be negative? That would make f(x,y) negative.

having trouble finding fY(y)

Just reverse the order of integration.