數學題,,,

圖片參考：http://i187.photobucket.com/albums/x22/cshung/7007102904120.jpg
　　　　　

f(x,y) can serve as the joint probability distribution of two random variables for any value of k if and only if the sum of f(x,y) for x=0,1; y=0,1,2 equals 1, and f(x,y) >= 0 for every possible values of x and y.

f(0,0)=0
f(0,1)=k(2-0)=2k
f(0,2)=2k(4-0)=8k
f(3,0)=0
f(3,1)=k(2-3)=-k
f(3,2)=2k(4-3)=2k

if k positive, f(3,1) < 0
if k negative, f(0,1) < 0
if k is zero, sum of f(x,y) for x=0,3; y=0,1,2 is not equal to 1

therefore, f(x,y) cannot serve as the joint probability distribution for any value of k