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I know that the Maximum Likelihood estimator for the parameter lambda in a poisson distribution is the sample mean.

However my understanding is that this is only the case when the only constraint on lambda is lambda > 0. How do I approach questions with constraints on MLE parameters such as this?

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for a(i) I am pretty sure the answer is 2, since that is the sample mean. However in a(ii) lambda cannot be more than 1.

Does this mean the MLE estimator for lambda is now simply 1 since that is the closest to 2 it can get?

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    $\begingroup$ You just follow the way you used to find value 2 (sample mean), you will see which value of lambda in (0, 1] that maximizes the (log) likelihood. $\endgroup$
    – TrungDung
    Commented Oct 27, 2020 at 8:12
  • $\begingroup$ Please add the self-study tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. Did you have any advances? tell us! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Mar 21, 2021 at 20:48

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