1. Suppose X follows an exponential distribution with =2. Determine the following:

a. P (X 2)

b. P (X 2)

c. Find the value of X such that P (X

2. The time between calls for a plumbing business is exponentially distributed with mean = 15 minutes.

a. What is the probability of no calls in a 30-minute interval?

b. What is the probability that the first call will arrive within the 5-min interval? and 10 min. after opening trades?

c. What is the probability that at least one call will arrive within the 10-minute interval?

d. Determine the length of the time interval such that the probability of a call X arriving in at least one interval is 0.90.

3. The time between taxi arrivals at an intersection is exponentially distributed with mean =10 min.

a. What is the probability of waiting for more than an hour for a taxi?

b. Suppose you already wait an hour for a taxi, what is the probability that a taxi will arrive within the next 10 minutes?

4. The life in hours of an electronic device is a random variable that follows an exponential distribution with the following density function:

f X -x /200 200