2. You have observed that a friend of yours arrives each IE255 PS late. You have thought about the problem and decided not to be nosy, but you bet with another friend of yours. After observing your friend for a semester, you to reach to the conclusion that your friend's amount of lateness in terms of minutes to the lecture may be following an Exponential distribution. Let t denote the time of arrival of your friend, and X = t-10:00 denote the random variable that indicates the tardiness, i.e. lateness, of your friend in minutes. Let X ~ Exponential(4). In each of the cases below, you get p TLs and lose p TLs if the outcome occurs respectively. First, calculate the probabilities then indicate whether you ought to or not take the bet. a) Outcome: X 5, P(X 5) b) Outcome: X 10|X 5, P(X 10|X 5) c) "Independent from the previous parts, assume that your friend drops her pencil frequently. If we denote the number of times your friend drops her pencil per five minutes as Y and that Y ~ Poisson (20). What is P(Y > 1)?