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.

Step 1 of 4</p>

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</p>

a) we have to find

=1-(1-)

=

=0.0067

Hence =0.0067

Step 2 of 4</p>

b) No, five minutes is not unusually long time to wait

Because the probability is small

It occurs for 67 times in 10000 samples

Step 4 of 4</p>

c)No, we can’t believe the claim

Because the probability is very small

And five minutes is not unusually long time to wait