The duration of a voice telephone call is an exponential random variable V with expected value E[V]=8 minutes, and the duration of data call is an exponential random variable D with expected value E[D] = d>8 minutes.

The null hypothesis is H0: a call is a voice call, while the alternative hypothesis is H1: a call is a data call.

The probability of a voice call is P[V]=0.8, while the probability of a data call is P[D]=0.2.

A binary hypothesis test measures T minutes, the duration of call. The decision is H0 if T≤t minutes. Otherwise, the decision is H1.

Write the formula for the false alarm probability as a function of t and d