4. (a) Let Xi,X ,x, be n observations from an N(u2) distribution, and define the estimators (i) Determine whether T and T2 are unbiased estimators of u. 4 points (ii) Compute the variances Var(Ti)...
Let X1,..., Xn be a random sample from a distribution. Suppose Ti (X),T2(X) and U(X) respectively are sufficient, minimal sufficient, and unbiased estimators for the parameter θ of the distribution. Let U1(X) = E U(X) T, (X), U2(X) = EU㈤ T2(X)] a. Show that U1(X) and U(X) are unbiased for θ. b. Show that U2(x)-E[Uj(X)ITLX] c. Show that U2 has a smaller variance than U
please answer with full soultion. with explantion. (4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
be a random sample from the density 16 1. Let Xi, . f(x; β) otherwise 8(1-/4). You may suppose that E(X)(/ (a) Find a sufficient statistic Y for B and Var(X) C21 C2] 031 (b) Find the maximum likelihood estimator B of B and show that it is a function (c) Determine the Rao-Cramér lower bound (RCLB) for the variance of unbiased (d) Use the following data and maximum likelihood estimator to give an approxi- 2.66, 2.02, 2.02, 0.76, 1.70,...
Hello, I need question 1 sections a,b,and c. Please make around a page long. CHAPTER 4 Techniques for Understanding Consumer Demand and Behavior 109 t effect. ed that managers be familiar with both approaches because each provides useful ues need to realize that marketing analysis builkds on the fundamental eco- of demand and elasticity. Marketers take these basie economie n Table 3.7 in goies and develop analyses of brand differentiation, market segmentation, and dct pricing, While some of the formal...