Question: Suppose a computer network experiences a certain volume of traffic in a given time period, where on average 5 users (independently) connect each minute. Let

Suppose a computer network experiences a certain volume of traffic in a given time period, where on average 5 users (independently) connect each minute. Let N(t) be the number of users connecting within t minutes and assume N(t) is a Poisson process with parameter , where Pr(N(t) = k) = ( ) ! , k = 0, 1, 2, ...

a. State the value of and compute the probability that 1 user connects in 2 minutes

b. Compute the probability that 4 users connect in 2 minutes

c. Compute the probability that between 0 to 3 users connect in 2 minutes

d. Compute the expected number of users connecting within 2 minutes

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