Each of 100 multiple-choice question on an exam has four possible answers, one of which is
correct. For each question, a student guesses by selecting an answer randomly.
(a) Specify the distribution of the student's number of correct answers.
(b) Specify the distribution of $(Y_1, Y_2, Y_3, Y_4)^T$, where $Y_j$ is the number of times the student
picked choice $j$, $j = 1, 2, 3, 4$.
(c) Find $E(Y_j)$, $var(Y_j)$, and $cov(Y_j, Y_k)$.