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 faults | 0 | 1 | 2 | 3 | 4 | 5 | >5 |
| number of lines | 38 | 30 | 16 | 9 | 5 | 2 | 0 |
(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.
