Problem 3 he mean 2 of a Poisson distribution is known to be either 1 or 2. One random observation X is available from the Poisson distribution Estimators : and 2: are dened as below: X: 0 X : l X 2 2 l 1.5 2 0 1 2 i ii (a) What are the mean and variance for each of 2: and xiv '? (Remember to work with both possible parameter values.) (b) Which of 2: or i: is the best estimator? Problem 4 Random variable has cdf F(x) = x", 0 0. Given the sample x] : 01, x2 : 08, x3 : 0.9 (:1) Find method of moments estimate '9':th . (b) Find maximum likelihood estimate 6\