Problem 121E

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

(a) What is the probability that you wait longer than one hour for a taxi?

(b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes?

(c) Determine x such that the probability that you wait more than x minutes is 0.10.

(d) Determine x such that the probability that you wait less than x minutes is 0.90.

(e) Determine x such that the probability that you wait less than x minutes is 0.50.

Solution

Step 1 of 5

Let X be the time between the arrivals of taxi

Here X is exponential random variable with mean of 10 min

Then

a) We have to find the probability that you wait longer than one hour for taxi

Here one hour=60 minutes

The cumulative density function of exponential distribution is

We have to find

=

=

=0.0025

Hence the probability that you wait longer than one hour for taxi is 0.0025