Let Y be the nth order statistic of a random sample of size n from Unif(0, 0). Let 0 has the prior pdf h(0) = BaB /0ß+1, 0 > a > 0, where a > 0, ß > 0. Find the Bayes estimator of 0 inder the squared orror loss

Q3) Let X1,X2,. X, be a random sample from the truncated exponential distribution with pdf: f(x,0) = Please else (a) Derive the method of moment estimator of 0; (b) Derive the MLE of 0. (c) Are the MOME and the MLE unbiased estimators for 0? (d) Compare the MSE of the MOME and the MLE for 0. Which one is a better estimator for 0

Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.

Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s^2is known.Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix using GLM

Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i + e_i where e_i are independent and identically distributed N(0, variance_e) randon variables i = 1,...,2.

Q4 Three electron emitters produce electron beams with changing kinetic energies that are uniformly distributed in the ranges [3,7+45], [2,5+45], and [4,10+45] (Roundup after multiplying by f). Let Y denote the total kinetic energy produced by these electron emitters. (a) Suppose that the three beam energies are independent. Determine the mean and variance of Y . (b) Suppose that the covariance between any two beam energies is -0.5. Determine the mean and variance of Y . (c) Compare and comment on the results in parts (a) and (b).

Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.

5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0. Compare the

28. Let X,..., X, be a random sample from EXP(6), and define ô, = X and Ô, = nX/(n + 1). (a) Find the variances of 6, and 8. (b) Find the MSES of é, and ô,. (c) Compare the variances of 0, and 8, for n= 2. (d) Compare the MSES of ô, and ô, for n = 2. (e) Find the Bayes risk of 6, using 8 - EXP(2).

Consider the one-way analysis of variance model Xij = µ + a; + Eij, i= 1,.., m, j= 1,..., ni, where ɛij ~ N(0,0²) are independent. Let n= n1 + · ·+ nm, ... ni 1 ni 1 X;. >Xii for i = 1,..., m, and X. = - ΣΣΧ. ni j=1 i=1 j=1 (a) Show that SS(TO) = SS(T) + SS(E), where SS(TO) = E E i=12j=1 (Xij – X..)², m m ni SS(T) Σι (X.-Χ.) and SS(E) -ΣΣ (Χ- X.) . i=1 i=1 j=1