Please solve all parts a-e. Please show all work for parts a-e.

a.) Let U be a Uniform[0,1]random variable. Find the expectation of the random variable 3(2^U).

b.) You arrive at the train station at 8 am. Train will arrive anywhere in between 8 am and 8:20 am. Given you already waited 5 min and the train did not arrive, what's the probability that you will wait for 5 more?

c.) Given the information in part b, now we still suppose you arrive at the train station at 8 am, but the train arrival time is an Exponential(1/2) random variable on the interval from 8 am to infinity, in hrs. Find the probability that you'll wait more than 50 min until the train arrives.

d.) In above setup, given you waited 2 hrs and the train did not arrive, find the probability that you will wait for at least 2 more hrs before the train arrives.

e.) The professor gives a random number of quizzes per week, in average 3 per week. Find the probability that over the next 2 weeks he will give no quiz.