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.

What is the sum of these mixed numbers 2 1/8 + 4 3/8

Two language majors, anna and megan, took exams in two languages. anna scored 85 on both exams. megan scored 74 on the first exam and 85 on the second exam. overall, student scores on the first exam had a mean of 82 and a standard deviation of 4, and the second exam scores had a mean of 71 and a standard deviation of 13. a) to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. so far, which of anna and megan qualify? b) which student's overall performance was better?

When y’all answer can y’all explain too !