3-141. The time between the arrival of e-mail messages at your computer is exponentially distributed with a mean of 2 hours. (a) What is the probability that you do not receive a message during a 2-hour period?

The probability that there was no messages received during a 2-hour period is 0.3679.

Step-by-step explanation:

Let the random variable X = time between the arrival of e-mail messages.

The random variable

The probability distribution function of exponential distribution is:

The mean of the distribution is, Mean = 2.

The value of λ is:

Compute the probability that there was no messages received during a 2-hour period as follows:

Thus, the probability that there was no messages received during a 2-hour period is 0.3679.

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