Final answer:
The expected value is 2.5, and the variance of the sum is 3.375.
Step-by-step explanation:
The expected value is the sum of the products of each outcome and its probability. Since all the outcomes (1, 2, 3, and 4) have an equal likelihood of occurring (1/4), the expected value is:
Expected value = (1/4) x 1 + (1/4) x 2 + (1/4) x 3 + (1/4) x 4
= 1/4 + 1/2 + 3/4 + 1
= 2.5
The variance of the sum can be calculated by finding the variance of each individual outcome and summing them. The variance of each outcome is given by:

where x is the outcome, E(X) is the expected value, and P(X) is the probability of that outcome happening.
The variance of the sum is:
Var(sum) = Var(1) + Var(2) + Var(3) + Var(4)


= 3.375