Let x have a probability density function (Poisson

distribution with mean (complete question is given in the picture attached)

i) Find the log-likelihood function.

ii) Determine the maximum-likelihood estimate

(MLE) for .

2) Let x have a probability density function (Pois- son distribution with mean 0) 0% exp(-0) x! x 20 pace = otherwise Suppose that n samples X1, ..., In are drawn independently according to p(a | 0). i) Find the log-likelihood function. ii) Determine the maximum-likelihood esti- mate (MLE) for 0