# Marginal from joint pdf

I am trying to learn probability theory through self study, so I have been working through the MIT open courseware problems. I am pretty stuck on the following one

How do we find the marginal pdf of $f_Y(y)$? I know we need to integrate the joint over $X$ but I don't see how to do it?

• Since this is self study you need the self study tag. Then we can provide hints to help you. – Michael R. Chernick Feb 11 '17 at 16:00

$p_Y(y) = \int_x p_{X,Y}(x,y) \, \mathrm{d}x$ $= \int_1^{2-y} \ 3/2 \ dx+\int_y^{1} \ 1/2 \ dx$