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Suppose that a biased sample variance was defined as: $2 n+1 and that the true population variance is o?. Calculate the following ratio to 4 decimal places where n= 9 E(S;) 02 Hint: If S^2 is UNBIASED then E(S2 ) = 02, write S2 in terms of $2Suppose that Y1, Ys, ..., Y, is a random sample from a Normal distribution with mean u and variance o? = 1. Find the numerical value of the variance of S? to 4 decimal places where n=11. Hint: Use the chi-sq sampling statistic, (n-1)s*2/sigma\"2 (From MS 7.8) A binomial experiment consisting of n trials resulted in Bernoulli observations y4, ys, . . . Y. Where: y; = 1 for success and O else. Suppose that the probability of success is p and the probability of failure is (1-p). WedefineY = 37" y; Find the moment estimator of p and evaluate the answer to 4 decimal places when n =10,andY =4 The likelihood in the case of continuous data is the Joint density expressed as a function of the unknown parameters. O True % O False Let Y7, Y5, ..., Y, bearandom sample of n observations such that they are all iid with the following density: e W/P fw)=q # 0, else yi >0 Find the maximum likelihood estimator for 3. Now submit the estimate of beta to 4 decimal places when the sample is y 0 = 0, else Find the following to 4 decimal places: AE(BMLE - B) Hint: f(y) is a gamma density with alpha = 2. Is the estimator unbiased?Let Y1, Y2, . .., Y'n be a random sample of n observations such that they are all iid with the following density: f (yi) = ; yi > 0 0, else Find the following to 4 decimal places: V(B MLE) when assuming that n =10, B = 2 Hint: Substitute / into V(B) and simplifySuppose Yi ~ Bin(n = 10, p) and a random sample of 20 observations were collected from repeating the Binomial. Use the MoM and the following information to calculate the estimate for p to 4 decimal places where Y = 150 = Y1 + Y2 + ... + Y20(From MS 7.12) Let 41, 2, . . . , Yn be a random sample of n observations from an exponential distribution with density fly) = { gTe upl 0, else Find the MoM estimator of /3, is it biased? O No O Yes Let 01 and 2 be two unbiased estimators for a parameter 0. If Var(01)