Statistics - Poisson distribution question.

[peripatein]

Hi,

Homework Statement

I am somewhat perplexed by the proposed solution to the following Statistics problem and was hoping one of you might be willing to help me settle this:
An operator receives phone calls between 8AM and 4PM at an average rate of 20 calls/hour. No call was received during the first 3 minutes. What is the probability that we shall have to wait at least one more minute before the first call is received?

Homework Equations

The Attempt at a Solution

Now, the book states it ought to be P(T≥1) = 1 - F_T(1) = e^-1/3.
My question is, why should it not have been 1 - [F(4) - F(3)], i.e. the complement of a call received between the 3rd and 4th minutes?
I'd appreciate it if any of you could explain this to me.

 

[Ray Vickson]

Hi,

Homework Statement

I am somewhat perplexed by the proposed solution to the following Statistics problem and was hoping one of you might be willing to help me settle this:
An operator receives phone calls between 8AM and 4PM at an average rate of 20 calls/hour. No call was received during the first 3 minutes. What is the probability that we shall have to wait at least one more minute before the first call is received?

Homework Equations

The Attempt at a Solution

Now, the book states it ought to be P(T≥1) = 1 - F_T(1) = e^-1/3.
My question is, why should it not have been 1 - [F(4) - F(3)], i.e. the complement of a call received between the 3rd and 4th minutes?
I'd appreciate it if any of you could explain this to me.

If T is the time of the first arrival, you want P{T > 4 | T > 3}, because you are told that the event {T > 3} occurred.

 

[peripatein]

Thank you, Ray! It's clearer now :-).