The time that it takes to service a car is an exponential random variable with rate 1. (a) if lightning mcqueen (l. m.) brings his car in at time 0 and sally carrera (s. c) brings her car in at time t, what is the probability that s. c.’s car is ready before l. m.’s car? assume that service times are independent and service begins upon arrival of the car. be sure to: 1) define all random variables used. 2) explain how independence of service times plays a part in your solution. 3) show all integration steps. (b) if both cars are brought in at time 0, with work starting on s. c.’s car only when l. m.’s car has been completely serviced, what is the probability that s. c.’s car is ready before time 2?

Look at the following graph of the given equation. determine whether the equation is a function. explain why or why not.

In a column proof the right column states your reasons

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?