Hello everyone! While doing the Week 2 quiz I got a bit stuck with the calculation of a mean value in a joint distribution table, where we have two variables, x and y, so I used “the gut feeling” to solve that particular question, but I really want to understand… Here is the table:
And the mean of x is:
μx=(0×0.2+1×0.1)+(0×0.1+1×0.6)=0.7
Which means that it depends on values of y and this is something I cannot get. I failed to find an explanation in the week videos also Could please someone explain, how to calculate the mean in these multi-variable distributions and why the mean of x depends on y also.
I changed the presentation of data and it helped me visualize it better:
X
0
0
1
1
Y
0
1
0
1
P
0.2
0.1
0.1
0.6
Now, the problem is the same as the one in the "Covariance of a Probability Distribution" video, around minute 6. For each of means of X and Y, you need to take a marginal distribution of the data, i.e., ignore the other variable. You found μX correctly. If we do the same thing for μY, we'll have:
μY = 0.2(0) + 0.1(1) + 0.1(0) + 0.6(1) = 0.7
In other words, E[ X ] = E[ Y ] = 0.7. Next, you need to calculate E[ XY ]:
Could please someone explain, how to calculate the mean in these multi-variable distributions and why the mean of x depends on y also.