Question

In: Statistics and Probability

3. The time T required to receive a message at node B from node A is...

3. The time T required to receive a message at node B from node A is an exponentially distributed random variable with mean 1/10 (milliseconds). The time T is measured from the moment that a message left node A to the moment that it was received by node B.

a) What is the probability that T exceeds 105 milliseconds?

b) What is the probability that a message is received after 200 milliseconds given that no message was received before 95 milliseconds? That is, calculate: P(T > 200 | T 95):

Expert Solution

We are given that T is exponentially distributed with mean 1/10 (millisecond).

and the pdf and cdf of T are given by

:

(t in milliseconds)

a)

The probability that T exceeds 105 milliseconds is given by:

b)

The probability that a message is received after 200 milliseconds given that no message was received before 95 milliseconds is given by:

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orchestra answered 1 year ago

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