Question 3: Ever craved an ice cream shake from the local drive-thru restaurant just to find out the ice cream machine is broken? WHY IS IT ALWAYS BROKEN?! Let the random Trarial'rle X represent the length of time (in days] between successive break downs of the ice cream machine at the local drive-thru restatn'ant. Suppose X follows an exponential distribution with l=.l]. a) What is the expected time between two successive breakdowns? [2 pts] b} What is the standard deviation of the time between successive breakdowns? [2 pts] c) What is the probability;r that the next ooeunence of the ice cream machine breaking down is at most 15 days? [5 pts] d} How many days represents the 30m percentile? [-tl pta] e) Suppose it has been two weeks {i.e.. 14 days] since the ice cream machine broke down last. Wt is the probability that it will be at least three weeks (trek. 21 days) until the ice cream machine breaks down\"? [5 pts]