Chapter 4.4, Problem 5E

For each of the following functions, determine the value of c for which the function is a joint pdf of two continuous random variables X and Y,

(a) $f\left(x,y\right)=cxy,0\le x\le 1,x^2\le y\le x$.

(b) $f\left(x,y\right)=c\left(1+x^{2}y\right),0\le x\le y\le 1$.

(c) $f\left(x,y\right)=cy{e}^x,0\le x\le y^2,0\le y\le 1$.

(d) $f\left(x,y\right)=c\sin \left(x+y\right),0\le x\le \frac{\pi }{2},0\le y\le \frac{\pi }{2}$.