ID: 18391Nhận biết (M1) The duration of a voice telephone call is an exponential random variable with expected value of minutes. The duration of a data call is an exponential random variable with expected value of minutes. The null hypothesis of a binary hypothesis test is “a call is a voice call”. The alternative hypothesis is “a call is a data call”. The probability of a voice call is and the probability of a data call is . Assume that the cost of a false alarm is units and the cost of a miss is units. A binary hypothesis test measures minutes, the duration of a call. Based on the observation of ,
(a) What are and , the likelihood functions of given and , respectively.
(b) Design a minimum cost hypothesis test.
(c) What is the average cost of the minimum cost policy?
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The duration of a voice telephone call is an exponential random variable with expected value of minutes. The duration of a data call is an exponential random variable with expected value of minutes. The null hypothesis of a binary hypothesis test is “a call is a voice call”. The alternative hypothesis is “a call is a data call”. The probability of a voice call is and the probability of a data call is . Assume that the cost of a false alarm is units and the cost of a miss is units. A binary hypothesis test measures minutes, the duration of a call. Based on the observation of ,
(a) What are and , the likelihood functions of given and , respectively.
(b) Design a minimum cost hypothesis test.
(c) What is the average cost of the minimum cost policy?
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