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JohnNarsuba
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Tyro
Asked: 2021-04-06T01:50:39+00:00 In: ,

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70 independent messages are sent from an electric tansmission center. Messages are processed sequentialy, one after another. The transmission tome of each message is exponential with a mean of 0.2 minute. Find the probability that all 70 messages are transmitted in less than 12 minutes

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  2. acedstud

    Given that the average transmission time for each message is 0.2 minutes, then the average transmission time for the 70 messages is 70 x 0.2 = 14 minutes. Thus, \mu=14.

    Let X be a random variable representing the transmission time of 70 messages, since X follows an exponential distribution, the probability that X is less than a value, x, is given by P(X<x)=1-e^{-mx}, where m=\dfrac{1}{\mu}.

    Thus, the probability that all 70 messages are transmitted in less than 12 minutes is given by P(X<12)=1-e^{-\frac{1}{14}\cdot12}=1-e^{-0.8571}=1-0.4244=0.5756.

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