Nhận biết (M1)

The duration of a voice telephone call is an exponential random variable with expected value minutes. The duration of a data call is an exponential random variable with expected value 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 . Based on (minutes) the duration of a call,

(a) Design a maximum a posteriori probability (MAP) test.

(b) Calculate the total error probability .

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