2. In a meteor shower, the waiting time from one meteor sighting to the next is exponentially distributed with rate it = 1 per minute, and waiting times between successive meteor sightings are independent. (a) You arrive at midnight and turn on the telescope. What is the pdf of the time you must wait to see two meteors? (This is the pdf of the sum S = T1 + T2 of two independent rv's T1 and T2 both having an Exp(l) distribution. Do you see how this statement uses the memoryless property?) (b) We know that the mean of the EXPO) distribution is % Show that the variance of the EprL) distribution is %. [[This is quite easy with the help of our handy calculus tip that f5\" 1'?" d! = k!.]] (C) Suppose we want to observe 100 meteors. Using the Central Limit Theorem (CLT), approximate the 90th percentile of the distribution of the time you will need to observe. (d) Suppose you are being charged 1 penny (i.e. $.01) per second to use the telescope, and you have just managed to scrape together $69.00 for this occasion. Use the CLT to approximate the probability that you will be able to observe at least 100 meteors before you must give up the telescope