Question Solved1 Answer 2. In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of 6 minutes? What is the median time between log-ons? Hint: This is the interval of time such that the probability of no log-ons during that interval is 0:5 .

DCW1LB The Asker · Probability and Statistics

2. In a large corporate computer network, user log-ons to the system can be modeled as
a Poisson process with a mean of 25 log-ons per hour.
What is the probability that there are no log-ons in an interval of 6 minutes?
What is the median time between log-ons? Hint: This is the interval of time such
that the probability of no log-ons during that interval is 0:5 .

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There are 25 log-ons per 60 minutes. Therefore 25/60 log-ons per minute. a) Let X be a random variable denoting number of log-on in 6 minutes  {:[X∼P(lambda=(25//60)**6)],[" or, "X∼P(lambda=2.5)]:} So in 6 minutes, if there is no log-on then, we are interested to find P(X=0) {:[P(X=x)=(e^(-lambda)lambda^(x))/(x!)],[" or, "P(X=0)=(e^(-2.5)2.5^(0))/(0!)],[" or, "P(X=0)=e^(-2.5)=0.0821]:} b)  Then probability of n ... See the full answer