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The number of faults over a period of time was collected for a sample of 100...

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Statistics

The number of faults over a period of time was collected for asample of 100 data transmission lines. We want to test if the datacome from a Poisson distribution.

number of faults012345>5
number of lines3830169520

(a) Assuming the number of faults for a data-transmission line,Yi , i = 1, . . . , 100, follows a Poisson distribution withparameter λ, find the maximum likelihood estimate of λ for thesedata.

(b) Test the hypothesis that the number of faults for adata-transmission line follows a Poisson distribution using thechi-squared test. Do we reject the null hypothesis at the 5%significance level? Hint: You should combine the observed data intoseveral groups such that expected frequencies are greater or equalto 5 for each group.

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