Suppose that x1, , xn form a random sample from a Poisson distribution for which the mean is unknown, ( 0) a Determine the M L E of , assuming that at least one of the observed values is different from 0 b Show that the M L E of does not exist if every observed value is 0

Question: Suppose that x1, . . . , xn form a random sample from a Poisson distribution for which the mean is unknown, ( >

Suppose that x1, . . . , xn form a random sample from a Poisson for which the mean θ is unknown, (θ > 0).
a. Determine the M.L.E. of θ, assuming that at least one of the observed values is different from 0.
b. Show that the M.L.E. of θ does not exist if every observed value is 0.

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