Final answer:
The distribution function Fₜ(t) for the time T between any two email messages arriving at the email server can be determined using the exponential distribution.
Step-by-step explanation:
The distribution function Fₜ(t) for the time T between any two email messages arriving at the email server can be determined by using the exponential distribution. In this scenario, the cumulative distribution function is given as P(X<x) = 1 -e^(-0.25x), where X represents the time between email messages.
To find the distribution function Fₜ(t), we need to calculate P(T<t) for a given time t. Since the exponential distribution is memoryless, the probability that a customer spends more than three minutes with a postal clerk can be found by calculating P(X>3) = 1 - P(X<3).
Using the given information, P(X<3) = 1 - (1 - e^(-0.25·3)) = e^(-0.75) ≈ 0.4724. Therefore, the distribution function Fₜ(t) for the time T between email messages can be written as Fₜ(t) = 1 - e^(-0.25t).