Consider xlambda Poissonlambda and lambda gamma2 1 where Px

Consider x|lambda ~Poisson(lambda) and lambda ~ gamma(2, 1) where: P(x| lambda) = e^- lambda lambda ^x/x!, lambda > Find the posterior distribution P(lambda|x) given the following observations x = {5, 6, 5, 10, 3, 9, 4, 4, 4, 12}, find summary statistics for lambda (mean, median, mode, standard deviation) and compute the 95% credible set for lambda.