Hello shdh,
In, this question we are testing the hypothesis that the number of claims, \(X\) follows a Poisson distribution.
We estimated \(\lambda\) using MLEs as:
\[\hat\lambda = 0.1658\]
So,
\[X\sim Poi(0.1658)\]
Now, using this we calculate the Expected frequencies as follows:
When the number of claims is 0, the expected frequency is = \(3420P[X=0] = 3420(e^{-0.1658}) = 2897.48\)
Now, we can calculate the rest of the probabilities in a similar fashion.
We are performing the chi-square goodness of fit test for our null hypothesis,
\(H_{0}: \) The given data conforms to a Poisson distribution.
As the test statistic was greater than the tabulated value, we rejected the null hypothesis and concluded that the given data does not conform to a Poisson distribution.
Hope this helps.
Kaustav.
Last edited by a moderator: Apr 11, 2016