ifiotdedepleamning di datsmachine vrartificialintelligencedx The Poisson distribution is defined as: P(X=k)=k!ke(k=0,1,2,) (a) Let X1Poisson(), and x1 be an observed value of X1. What is the likelihood given ? [2 pts ] (b) Now, assume we are given n such values. Let (X1,,Xn)Poisson() where X1,,Xn are i.i.d. random variables, and x1,,xn be observed values of X1,,Xn. What is the likelihood of this data given ? You may leave your answer in product form. [3 pts] (c) What is the maximum likelihood estimator of ? [10 pts ]