If f(x,y)=ky(2y-x) for x=0,3; y=0,1,2 can serve as the joint probability distribution of two random variablesThen Σf(x,y)=f(0,0)+f(0,1)+f(0,2)+f(3,0)+f(3,1)+f(3,2)=0+2k+8k+0+(-k)+2k=1,and f(x,y)≧0 for any set of x and yBut when x=3,y=1,f(3,1)=k*1* (2-3)=-k≧0 k≦0 which can not fit Σf(x,y)=1Therefore, there is no value of k for which f(x,y)=ky(2y-x) for x=0,3; y=0,1,2 can serve as the joint probability distribution of two random variables
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If f(x,y)=ky(2y-x) for x=0,3; y=0,1,2 can serve as the joint probability distribution of two random variablesThen Σf(x,y)=f(0,0)+f(0,1)+f(0,2)+f(3,0)+f(3,1)+f(3,2)=0+2k+8k+0+(-k)+2k=1,and f(x,y)≧0 for any set of x and yBut when x=3,y=1,f(3,1)=k*1* (2-3)=-k≧0 k≦0 which can not fit Σf(x,y)=1Therefore, there is no value of k for which f(x,y)=ky(2y-x) for x=0,3; y=0,1,2 can serve as the joint probability distribution of two random variables