(a) You are a college student and you are yet to declare your major. You are torn between two majors - mathematics and statistics. You keep changing your mind at the rate of A times an hour. If you are considering mathematics for your major now, what is the probability that you are considering mathematics for your major when your friend ask you at time T (hour)? (Hint: Recall that 1+x+2+3 + 2 - = e. Hence, we find that 1x+32- Coming the two equations, we also see that 1+3+ ete and +3 2! ++ 5 = 3! 2 e--.) (b) In the same set-up, you are thinking about changing the major at the rate of A times per hour. But at each time you think about changing your major, you change your major with probability p, and do not change your major with probability 1-p. If you are considering mathematics for your major now, what is the probability that you are considering mathematics for your major when your friend ask you at time T (hour)?