Exponential distribution 6.12 It is 9:00 p.m. The time until Joe receives his next text message has an exponential distribution with mean 5 minutes. (a) Find the probability that he will not receive a text in the next 10 minutes. (b) Find the probability that the next text arrives between 9:07 and 9:10 p.m. (c) Find the probability that a text arrives before 9:03 p.m. (d) A text has not arrived for 5 minutes. Find the probability that none will arrive for 7 minutes. 6.14 Derive the mean of the exponential distribution with parameter . 6.15 Derive the variance of the exponential distribution with parameter . 6.17 The time each student takes to finish an exam has an exponential distribution with mean 45 minutes. In a class of 10 students, what is the probability that at least one student will finish in less than 20 minutes? Assume students' times are independent. 6.21 Suppose X  Exp(). Find the density of Y = cX for c > 0. Describe the distribution of Y .