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Magazine Problem 80
Suppose \(X\) is Poisson distributed with parameter \(\lambda=0.2\). (a) Find \(P(X<3)\). (b) Find \(P(2 \leq X \leq 4)\).
Problem 81
Suppose \(X\) is Poisson distributed with parameter \(\lambda=1.5\). Find the probability that \(X\) exceeds \(3 .\)
Problem 82
Suppose \(X\) is Poisson distributed with parameter \(\lambda=1.2\). Find the probability that \(X\) is at most 3 .
Problem 83
Suppose \(X\) is Poisson distributed with parameter \(\lambda=2\). Find the probability that \(X\) is at least \(2 .\)
Problem 84
Suppose \(X\) is Poisson distributed with parameter \(\lambda=0.6\). Find the probability that \(X\) is less than \(3 .\)
Problem 85
Suppose the number of phone calls arriving at a switchboard per hour is Poisson distributed with mean 7 calls per hour. Find the probability that no phone calls arrive during a certain hour.
Problem 86
Suppose the number of phone calls arriving at a switchboard per hour is Poisson distributed with mean 3 calls per hour. (a) Find the probability that at least one phone call arrives between noon and \(1 \mathrm{P.M}\). (b) Assuming that phone calls in different hours are independent of each other, find the probability that no phone calls arrive between noon and 2 P.M.
Problem 87
Suppose the number of typos on a book page is Poisson distributed with mean \(0.5\). Find the probability that there is at least one typo on a given page.
Problem 88
Suppose the number of typos on a book page is Poisson distributed with mean \(0.1\). (a) Find the probability that there are no typos on a page. (b) How many pages with typos do you expect in a 200 -page book?
Problem 89
The number of amino acid substitutions in a given sequence is Poisson distributed with mean 3 . What is the probability of at least two substitutions?
