f(x,y)=(x+y)/30 for x=0,1,2,3; y=0,1,2
here is the chart for the probability of f(x,y), i.e., P(0,0)=0, P(1,0)=1/30, P(1,1)=2/15 ...
0 1/30 1/10 1/5
1/30 2/15 3/10 8/15
1/10 3/10 3/5 1
Find E[2X-Y]
E[2X-Y]=2E[X]-E[Y]
g(x)=1/30*[(x+0)+(x+1)+(x+2)]=(x+1)/10
h(y)=1/30*[(y+0)+(y+1)+(y+2)+(y+3)]=(2y+3)/15
2E[X]=4
E[Y]=19/15
So E[2X-Y]=41/15,
But when I use the chart, the answer is 31/10. So I don't know why, can you tell me how will you gonna do to solve this problem? Thanks
Lets compute the maginal distributions, which are the last row and column of the following table:
The sums of the last row and column should both be 1 which should be the sum of all the elements in the table if this truly represents the joint distribution of (x,y), but they do not, they are .
So there is an error in your table.
.