Question

An operations analyst counted the number of arrivals per minute at an ATM in each of 30 randomly chosen minutes. The results were: 0, 3, 3, 2, 1, 0, 1, 0, 0, 1, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1. For the Poisson goodness-of-fit test, what is the expected frequency of the data value X

Answer 1

Explanation:

since Poisson distribution parameter is not given so we have to estimate it from the sample data. The average number of of arrivals per minute at an ATM is

`\hat{\lambda}=\bar{x}=(\sum x)/(n)=(30)/(30)=1`

So probabaility for
`\mathrm{X}=1` is

`P(X=1)=(e^(-\lambda) \lambda^(x))/(x !)=(e^(-1) \cdot 1^(1))/(1 !)=0.3679`

So expected frequency for
`X=1` is
`0.3679^(*) 30=11.037` (or
`\left.11.04\right)` .