Question

You are waiting for a friend to call you and that the time you wait in minutes has an exponential

distribution with parameter

λ=0.1.

(a) What is the expectation of your waiting time?

(b) What is the probability that you will wait longer than 10 minutes?

(c) What is the probability that you will wait less than 5 minutes?

(d) Suppose that after 5 minutes you are still waiting for the call. What is the distribution of your additional

waiting time? In this case, what is the probability that your total waiting time is longer than 15 minutes?

(e) Suppose now that the time you wait in minutes for the call has a U (0, 20) distribution. What is the

expectation of your waiting time? If after 5 minutes you are still waiting for the call, what is the distribution of your

additional waiting time?

Answer 1

Answer:

Suppose that you are waiting for a friend to call you and that the time you wait in minutes has an exponential distribution with parameter

Let X denote waiting time

The pdf of X is given by

otherwise

The cdf of X is given by

  

  

a)

The expectation of your waiting time is

Minutes

b)

Probability that you will wait longer than 10 minutes

  

  

c)

Probability that you wait less than 5 minutes

d)

Suppose that after 5 minutes you are still waiting for the call.

The distribution of your additional waiting time has exponential distribution.

Probability that your total waiting time is longer than 15 minutes

e)

Suppose now that the cal has a U(0,20) distribution.

Let Y denote waiting time

Then the pdf of Y is,

elsewhere

The expectation on of your waiting time