Mathematics, 21.12.2020 20:00 edmundg2238
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.
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