Find directly the expected value and the variance of : Recall that xi ....xn are assumed...

Question

Question

Find directly the expected value and the variance of :

Σ JE 3π .2 σ i-1 ΣΕ1 Σ

Recall that x_i ....x_n are assumed to be non random and that , yi=Bax Ei, i= 1....n with €1...EiidN (0, o

Answer 1

Answer #1

ni yi 2 a,bicis Constant SE ay)-cEy) ECE)- i Elyi) .iE (pxi+ei) ECatby) atbEly)? Eler)- 111 C Exi(Bait ECei) =1 Ans Var C) x

Answer 2

Similar Homework Help Questions

3. Let Xi, . . . , Xn be iid randoln variables with mean μ and...

3. Let Xi, . . . , Xn be iid randoln variables with mean μ and variance σ2. Let, X denote the sample mean and V-Σ, (X,-X)2. (a) Derive the expected values of X and V. (b) Further suppose that Xi,-.,X, are normally distributed. Let Anxn ((a)) an orthogonal matrix whose first rOw 1S be , ..*) and iet Y = AX, where Y (Yİ, ,%), ard X-(XI, , X.), are (column) vectors. (It is not necessary to know aij...
Readings: Review for the 5 properties of expected value and variance e iid. Recall that ii.d....

Readings: Review for the 5 properties of expected value and variance e iid. Recall that ii.d. stands for independent and identically distributed.) Since have the same expected value and variance. Le 5. Let X,... Xn, b 1. ..., Xn all have the same distributi E(X1)-: μ and Var(X1) σ. Find the following in terms of μ and σ. (a) E(X). Note this is not pH (b) E0%XYn). (c) Now, define W by Find E(W) and Var(W).
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the dist...

Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0} complete? 2. Is PCH)〈1) the same for all σ ? 3. Find a sufficient statistic for σ. 4. Is the sufficient statistic from (c) also complete!? Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0}...

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1...

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is an approximate 99% confidence interval for the intercept of the line of best fit? We have a dataset with n= 10 pairs of observations (ri, Yi), and n n Σ Xi = 683, 2 yi...
Xn are independent normal variates with the same variance σ, but with Suppose that Xi, X2,...

Xn are independent normal variates with the same variance σ, but with Suppose that Xi, X2, different means, Xi ~N(pbi,ơ2), for i-1.2, n where bi, b,.. k constants. (a) Find expressions for the MLE of μ and σ. You need not show the second derivative conditions (b) Suppose that b,-b2-...-bn. Find a simplified expression for the MLE of μ (c) Suppose that b,-b2-...-bn-1, and , is known. Find the MLE ofơ
3. [6 pts] Let Xi, . . . , Xn be a random sample from a distribution with variance σ2 < oo. Find cov(X,-x,x) for i 1,..,n. 3. [6 pts] Let Xi, . . . , Xn be a random sample from a distribu...

3. [6 pts] Let Xi, . . . , Xn be a random sample from a distribution with variance σ2 < oo. Find cov(X,-x,x) for i 1,..,n. 3. [6 pts] Let Xi, . . . , Xn be a random sample from a distribution with variance σ2

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1...

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is the coefficient of correlation for this data? We have a dataset with n= 10 pairs of observations (li, yi), and n n Σ ti = 683, Σ9: = 813, i=1 η α? = 47, 405,...
5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J, 1,,-1, , n. OV&.for any two random variables X and Y)...

5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J, 1,,-1, , n. OV&.for any two random variables X and Y) or each 1, and (11 CoV(X,Y) var(x)var(y) (Recall that p vararo 5. Let X1,X2, . , Xn be a random sample from a distribution with finite variance. Show that (i) COV(Xi-X, X )-0 f ) ρ (Xi-XX,-X)--n-1, 1 # J,...
3. Let X1, . . . , Xn be iid random variables with mean μ and...

3. Let X1, . . . , Xn be iid random variables with mean μ and variance σ2. Let X denote the sample mean and V-Σ,(X,-X)2 a) Derive the expected values of X and V b) Further suppose that Xi,...,Xn are normally distributed. Let Anxn - ((a) be an orthogonal matrix whose first row is (mVm Y = (y, . . . ,%), and X = (Xi, , Xn), are (column) vectors. (It is not necessary to know aij for...

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1...

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is an approximate 95% confidence interval for the mean response at x0 = 90? We have a dataset with n = 10 pairs of observations (li, Yi), and n n Σ Xi = 683, Yi =...