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Stats: MLE's From Partial Data (Poisson) watch

    • Thread Starter

    Any help with this question would be appreciated. Thanks

    The number of breakdowns in a manufacturing process may be assumed to follow a Poisson distribution with parameter \lamda.

    During a 30 day period it was observed that on exactly 9 days there were no breakdowns. On the remaining 21 days all that is known is that there was at least one breakdown. Find the MLE of \lamda

    (Sorry I gave up with latex couldn't get it to work...suppose, people know the probability function p(x) well though..)

    \large P (\large X = 0)=\dfrac {e^{-\lambda}\lambda^r}{r!}

     =\frac {9}{30}

    \frac {9}{30} = e^{-\lambda}

    \ln \frac {9}{30} = {-\lambda} \ln e

    And you can find the MLE of the mean. This is just a wild guess. I think this is correct

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