Bruce is at a cafe watching people walk past while he works. He decides to model the number of people that pass him. Over the time he is there he sees a mean of 5 people per minute. You can assume that the number of people per minute is an independent variable. (a) Why should Bruce use the Poisson distribution for the number of people he sees per minute and what is the relevant parameter? (b) Using this distribution, what is the probability that Bruce will be passed by more than 7 people in a minute? (c) What is the probability that Bruce will have a minute where no-one passes him?
Bruce is at a cafe watching people walk past while he works. He decides to model the number of people that pass him. Over the time he is there he sees a mean of 5 people per minute. You can assume that the number of people per minute is an independent variable. (a) Why should Bruce use the Poisson distribution for the number of people he sees per minute and what is the relevant parameter? (b) Using this distribution, what is the probability that Bruce will be passed by more than 7 people in a minute? (c) What is the probability that Bruce will have a minute where no-one passes him? (d) Bruce has seen no-one for 1 minute and 30 seconds. How long does he expect to wait for the next person?
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