Assume the number of users of a bank machine in a 5 minute interval is Poisson distributed with a parameter of 2.5. Compute the probabilities, that in a particular 5 minute interval: (a) someone uses the machine.

Assume the number of users of a bank machine in a 5 minute interval is Poisson distributed with a parameter of 2.5. Compute the probabilities, that in a particular 5 minute interval: (a) someone uses the machine.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

6. Assume the number of users of a bank machine in a 5 minute interval is Poisson distributed
with a parameter of 2.5. Compute the probabilities, that in a particular 5 minute interval:
(a) someone uses the machine,
(b) more than one person uses the machine,
(c) 3 or more people use the machine.

Expert Solution

Step 1

Let us denote X as the number of users of a bank machine in a 5 minute interval follows Poisson distribution with parameter of 2.5

That is, $λ = 2.5 p e r 5 m i n u t e i n t e r v a l$ .

The PMF for X is,

$P (X = x) = \frac{e^{- λ} λ^{x}}{x!} = \frac{e^{- 2.5} * 2 . 5^{x}}{x!}, x = 0, 1, 2, . . .$

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