Let x1, x2, . . . , xn be the observed values from a random sample from X P oisson(). a) [2 marks] Compute the method of moments estimate of the parameter . b) [3 marks] Compute , the maximum likelihood estimate of the parameter . c) [3 marks] Compute the Fisher information for from a sample of size n. d) [7 marks] Construct an asymptotic hypothesis test (although n = 10) with = 0.05, to test the hypotheses H0 : = 5 against H1 : = 5, using the following data: The 10 observations are {6, 11, 6, 5, 3, 12, 6, 6, 10, 5} In your answer, include the formula for the test statistic and the null distribution. State the asymptotic result that you are using. Give an exact expresssion for your P-value and sketch a curve shading the region corresponding to the P-value. Then give a statement of your conclusion in plain language. You may wish to use one of the quantiles given here from the normal and exponential distributions. > qnorm(0.95) [1] 1.644854 > qnorm(0.90) [1] 1.281552 > qnorm(0.975) [1] 1.959964 > qexp(0.95,5) [1] 0.5991465 > qexp(0.90,5) [1] 0.460517 > qexp(0.95,1/5) [1] 14.97866 > qexp(0.90,1/5) [1] 11.51293