If {xt } is stationary with E [xt] = 0 and corr(xt , xt −1) = rho1, show that the best linear predictor of xt based on xt −1 is rho1xt −1. (You will need to use calculus to do this problem. Here are some hints. First, define the random variables Y = xt , X = xt −1. Consider any linear predictor Yˆ = a + bX , where a and b are any numbers. Consider the mean squared forecasting error, MSE = E [Y − Yˆ] 2 = E [Y − (a + bX )]2.

Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.

A+b= 17, ab=70, find the value of |a-b|