Consider X, Y with joint density
fX,Y (x,y) = sech2x/(y+1)2
for x ≥ 0 and y ≥ 0,
and fX,Y (x,y) = 0 otherwise. Find P(X ≤ 2,Y ≤ 2). (The function "sech" is the hyperbolic secant, which should be familiar to many readers who recently completed a course in calculus. Other readers may choose to skip this exercise, because sech will make very few appearances in the densities that we consider in this text.)