an expectation can always be distributed over a finite sum a

an expectation can always be distributed over a finite sum

a) true

b) false

Solution

False.

In the apparent case where the probability distribution is discrete and specified for a finite set of variables, there is an inherent assumption that the probability of the rest of the variables is zero. Therefore, zero is multiplied with the value of those variables while finding the expectation, and they don\'t feature in the sum. So while practically the sum is over a finite set, theoretically the expectation cannot be distributed over a finite sum