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Problem 105: If a bank receives on the average α = 6 bad checks per day, what are the probabilities that it will receive (a) 4 bad checks on any given day?
(b) 10 bad checks over any 2 consecutive days?

Problem 105: If a bank receives on the average α = 6 bad checks per day, what are the probabilities that it will receive (a) 4 bad checks on any given day?
(b) 10 bad checks over any 2 consecutive days?


Solution:


Poisson distribution, $f(x;\lambda )=\frac{{\lambda }^{x}{e}^{-\lambda }}{x!}$

a. 4 bad checks on any given day
Given that $x=4, \lambda = \alphaT = 6\dot 1 = 6$
$f(4;6 )=\frac{{6 }^{4}{e}^{-6 }}{4!} = 0.134$

b. 10 bad checks over any 2 consecutive days
Given that $x=10, \lambda = \alphaT = 6\dot 2 = 12$
$f(10;12 )=\frac{{12 }^{10}{e}^{-12 }}{10!} = 0.104837$

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