Given:
The joint probability density function of X and Y is:
with bounds .
Question: Find the marginal density of X.
In the solutions key, when they find the marginal density of X they use the limits of integration .
Why do they do this and not use as the limits?
Have you tried drawing the region over which the given joint pdf is non-zero? Draw the lines y = x and y = -x. The region is the area above the V-shape, that is the region above the line y = x from x = 0 to x = oo and the region above the line y = -x from x = 0 to x = -oo. This region is alternatively defined by the area above y = |x|.