quick please

= 6. Let x = (21,..., In) denote a realised sample from a Poisson distribution with unknown para- meter 8 (0,0). The likelihood of a single observation xk E N is k L(0:0) exp(-0). *R! Assume that observations are i.i.d. given the value of 0. (a) Let a, 8 > 0. Assuming a Gamma(a, b) prior for e, derive the posterior distribution for a given the observed data r. [3 marks] (b) Consider the posterior mean as an estimator of the parameter 8. What can you say about the bias of this estimator? Can the posterior variance also be used as an estimator of e? [3 marks] [Total 6 marks] [END OF PAPER]