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.

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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.
Transcribed Image Text: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 per 5 minute interval.

The PMF for X is,

PX=x=e-λλxx!              =e-2.5*2.5xx!, x=0,1, 2, ...

 

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