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

let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)W

A random sample of n, 20 winter days in Denver gave a sample mean pollution index x, = 43. Previous studles show that o,- 10. For Englewood (a suburb of Denver), a random sample of n, - 19 winter days gave a sample mean pollution Index of x, = 37. Previous studies show that g, -13. Assume the pollution Index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) what is the level of significance? State the null and alternate hypotheses. (b) what sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard devtations. O The standard normal. We assume that both population…

For a given set of bivariate data, the following result n²100, EX= 5000; EY : 10000; EX2 - 26000; =1010000 and EXY =516000. Ci) Find the predicted value of Y when x = 60. (i) what is the predicted value of the x when Y = 80 (1) Calcutule mie coefficint of Correlation between & and Y. 2ملاع

The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation

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

The number of clients a store has during a week is Poisson distributed with - 25. The amount of money spent by each client follows a random = el,000t+250t2. Assuming the mean A variable with moment generating function o(t) independence between the number of clients, and the amount of money spent by each client. Find the mean and variance of the amount of money received by the store every week.