Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased
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Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?
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- Suppose that there are two assets that are available for investment and an investor has the following expected utility: EU = E(R,)– 0.5Ao, where expected return and standard deviation are expressed in decimals. For example, if expected return is 25%, standard deviation is 15%, and risk aversion is 5, expected utility is computed as: EU = 0.25 – 0.5×5x 0.15 = 0.1938 Now, assume that there is no other instrument (such as the risk-free security) available. Then, derive the analytical expressions for the optimal portfolio weights of the first and the second assets for this specific investor. (Hint: We are not talking about a numerical response here. Rather, you are asked to derive mathematically how you would compute for the optimal portfolio.)Regarding the parameters estimated in a simple linear regression, it is true that:a. β0 has maximum variance. b. var(β0) = σ (1/n + x̄2 / Sxx) c. β0 is biased. d. can be estimated through y (with up bar) - β0(x̄) Why? Thanks(x₂-μ)² 4(0²)² condition for deriving the estimator for the variance. Consider True a log L 062 False n 20² + i=1 (2) = 0. This is a first order
- 9. If the moment generating function of X is M(1) = 2 find the mean, variance and p.d.f. of X.A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. (a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 33 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 4,579.5465 791.5050 AgeMed -27.292 12.1893 Bankrupt 19.5612 12.0754 FedSpend -0.0132 0.0116 HSGrad% -27.5839 7.1731 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 33 d.f? (Round your answer to 3 decimal places.) t-value = (b-2) Choose the correct option.…A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. A) What are the appropriate null and alternative hypotheses to compare the means of the two groups? B) What is the appropriate test procedure for the hypotheses in Problem A? C) Carry out the test in Problem B using the criticalvalue method. D) Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke.
- We know that the point estimator o` is an unbiased estimator for the parameter 0 if E(e') = 0.If the estimator is biased (not unbiased), then the difference E(O) – 0 is called the bias of the estimator e and is denoted by Bias(e'). That is,i.i.d. Suppose that X₁,..., Xn Po(A) with n > 5. Consider the following two estimators of X: Which of the following is/are correct? • (1) Â₁ is unbiased. • (11) Â₂ is unbiased. • (III) Var(Â₁) < Var(Â₂). Select one: O A. None of the others O B. (I), (II) and (III) O C. (II) only O D. (1) only O E. (1) and (II) only Â₁ Â2₂ = n n Xi, (X₁ + 4X₂ + X3).9. Show that if t is a consistent estimator of 0, then ť is a 6. consistent estimator of 0'.
- In an effort to isolate the determinants of absenteeism, Jacob estimates two different regressions, A and B, using time series data. The R2 is 0.63 for regression A and 0.91 for regression B. Which is the superior regression? Explain your reasoning.An internet provider wants to see if male and female college students spend a different amount of time online each day. In a random sample of 200 male college student shows the mean was 85 minutes with σ = 15 minutes. Another sample of 250 female college students has a mean of 81 minutes and σ = 17 minutes. Is there enough evidence to prove the claim at α = .05.How was the correct answer of 12.5000 and 2.0833 attained?