Someone claims that the waiting time, in minutes, between hits at a certain website has the exponential distribution with parameter λ = 1.

a. Let X be the waiting time until the next hit. If the claim is true, what is P(X ≥ 5)?

b. Based on the answer to part (a), if the claim is true, is five minutes an unusually long time to wait?

c. If you waited five minutes until the next hit occurred. would you still believe the claim? Explain.

Solution

Step 1 of 4

The waiting time of hitting the website is exponentially distributed with

Let X is the waiting time of the next hit

The pmf of exponential distribution is

The CDF of exponential distribution is

Step 1 of 4

a) we have to find

=1-(1-)

=

=0.0067

Hence =0.0067