exercise:E1276e15ca: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> When John Kemeny was chair of the Mathematics Department at Dartmouth College, he received an average of ten letters each day. On a certain weekday he received no mail and wondered if it was a holiday. To decide this he computed the probability...") |
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When John Kemeny was chair of the Mathematics Department at Dartmouth College, he received an average of ten letters each day. On a certain | |||
Department at Dartmouth College, he received an average of ten letters each day. On a certain | |||
weekday he received no mail and wondered if it was a holiday. To decide this he | weekday he received no mail and wondered if it was a holiday. To decide this he | ||
computed the probability that, in ten years, he would have at least 1 day without any | computed the probability that, in ten years, he would have at least 1 day without any | ||
Latest revision as of 00:10, 14 June 2024
When John Kemeny was chair of the Mathematics Department at Dartmouth College, he received an average of ten letters each day. On a certain weekday he received no mail and wondered if it was a holiday. To decide this he computed the probability that, in ten years, he would have at least 1 day without any mail. He assumed that the number of letters he received on a given day has a Poisson distribution. What probability did he find? Hint: Apply the Poisson distribution twice. First, to find the probability that, in 3000 days, he will have at least 1 day without mail, assuming each year has about 300 days on which mail is delivered.