3. A multiple-choice examination has 10 questions, each with 4 possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. Let X denote the number of questions he answers correctly. (a) Write down the sample space of X. Does X follow a binomial distribution? If it does, write down the two parameters (n and p) of this binomial distribution. If it does not, explain why. (b) For some arbitrary & in the sample space of X, find the probability P(X = k).(c) What is the expect value E(X) and standard deviation o of X? (d) What is the probability that he gets an A in this exam, that is he answers at least 9 questions correctly