1. {25 points} In autumn. leaves of a tree fall to the ground according to a Poisson process with rate 5 per hour. There are 6 independent trees in a block and their fallen leaves are swept by a cleaner. The leaves are swept twice a day. one at 10:00. the other at 22110. (a) (6 points) What is the probability that exactly 30 leaves fall within 1 hour? [b] (6 points} What is the expected nuniebr of leaves swept each time? [c] (6 points] Start counting at 10:00. Given that exactly 5 leaves have fallen by lfl:3[l1 what is the expected number of fallen leaves by 11:00? (d) {7 points} Also start counting at 10:00. What is the expected time that the 10th leaf falls given that exactly 5 leaves have fallen by 10:30"