EXERCISE 1 The life of a certain type of automobile tire is normally distributed with mean 34000 miles and standard deviation 4000 miles. a. What is the probability that such a tire lasts over 40000 miles? b. Given that one of these tires has survived more than 30000 miles, what is the conditional probability that it survives for more than another 10000 miles? c. Find the probability that 2 out of 5 randomly selected tires will have lifetime 1.96 standard deviations above the mean. EXERCISE 2 Suppose that the lifetime of an electronic component follows an exponential distribution with parameter = 0.10. a. Find the probability that the lifetime is less than 10. b. Find the probability that the lifetime is between 5 and 15. c. Find t such that the lifetime is greater that t is 1%. EXERCISE 3 Suppose the a random variable X follows a Gamma distribution with parameters Alpha= 2, Beta= 0.5 a. Find P(x<1)

b. Find P(x<2| x>1).

EXERCISE 4

Suppose that an average of 45 customers per hour arrive at a shop according to a Poisson process. What is the probability that the shopkeeper will wait more than 8 minutes before three customers arrive?