Chapter 4.1, Problem 1E

For each of the following functions, determine the constant c so that $f\left(x,y\right)$ satisfies the conditions of being a joint pmf for two discrete random variables X and Y:

(a) $f\left(x,y\right)=c\left(x+2y\right),x=1,2,y=1,2,3$.

(b) $f\left(x,y\right)=c\left(x+y\right),x=1,2,3y=1,\mathrm{...},x.$

(c) $f\left(x,y\right)=c,x$ and y are integers such that 6x+y8. Oy5.

(d) $f\left(x,y\right)=c{\left(\frac{1}{4}\right)}^x{\left(\frac{1}{3}\right)}^y,x=1,2,y=1,\mathrm{2.....}$