We randomly select two students in a row with replacement, and we observe the value of the variable on each selected student. The values of will be denoted by 0 (for None), 1 (for One), 2 (for Two), and 3 (for Three). With this notation, each outcome of the experiment is a pair (1, 2) where each can be any of the values 0, 1, 2 or 3.

a. Construct a table that shows each possible outcome (1, 2) with the corresponding probability (1, 2).

b. Find the mean and standard deviation of the average value = (1 + 2)2 defined on the sample space of all samples (1, 2) with their probabilities (1, 2).