People arrive at a party according to a Poisson process of rate 30 per hour and...

People arrive at a party according to a Poisson process of rate 30 per hour and remain for an independent exponential time of mean 2 hours. Let X(t) be the number of people at the party at time t (in hours) after it started. Compute E[X(t)] and determine how long it takes to have on average more than 40 people at the party.

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orchestra answered 2 years ago

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α= 8 per hour

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Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t. What is the probability that at least 7 small aircraft arrive during a 1-hour period? What is the probability that at least 11 small aircraft arrive during a 1-hour period? What is the probability that at least 23...

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