Question

for example,given joint pdf of function is 2x
but intervals are 0<x<y<2. (it may be invalid pdf)    When i find marginal pdf of y,i will take interval of (0,y) and integrate it with respect to x,(x,2) and integrate it with respect to y. Do i need to use interval of 0<x<2 in any circumstance?

Answer 1

if support is 0 < x< y < 2

then for finding marginal pdf of y

$f(y) = \int f(x,y) dx$

here x vary from 0 to y

$f(y) =\int_{0}^{y} f(x,y) dx$

simlarly for marginal pdf of x

$f(x) =\int_{x}^{2} f(x,y) dy$

you do not need to use 0 < x< 2 here