Question (3): Point Estimation of Parameters and Sampling Distributions [35 points] 1) Suppose that 8, and...

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Question (3): Point Estimation of Parameters and Sampling Distributions [35 points] 1) Suppose that 8, and ₂ are estimators of the parameter 8. We know that E(8₁) = 0, E(8₂) = 8/3, V(8₂) = 10, V(8₂) = 4. For which value of the parameter 8 is better than 8₂? In what sense is it better? II) Let X be a geometric random variable with parameter 0 < p < 1, where f(x)= (1-p)* ¹p, x = 1,2,.... The mean and variance of X are 1/p and (1-P)/p², respectively. Based on a random sample of size n, find an estimator of p by: a) the method of moments, and b) the method of maximum likelihood estimation. III) Suppose that X-N(u, 40), and let the prior density for u be N(4,8). For a random sample of size 25, the value * = 4.85 is obtained. What are the maximum-likelihood and Bayes estimates of µ? Question (3): Point Estimation of Parameters and Sampling Distributions [35 points] 1) Suppose that 8, and ₂ are estimators of the parameter 8. We know that E(8₁) = 0, E(8₂) = 8/3, V(8₂) = 10, V(8₂) = 4. For which value of the parameter 8 is better than 8₂? In what sense is it better? II) Let X be a geometric random variable with parameter 0 < p < 1, where f(x)= (1-p)* ¹p, x = 1,2,.... The mean and variance of X are 1/p and (1-P)/p², respectively. Based on a random sample of size n, find an estimator of p by: a) the method of moments, and b) the method of maximum likelihood estimation. III) Suppose that X-N(u, 40), and let the prior density for u be N(4,8). For a random sample of size 25, the value * = 4.85 is obtained. What are the maximum-likelihood and Bayes estimates of µ?

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For the second question let X1 X2 Xn be a random sample of size n from the geometric distribution wi... View the full answer