Consider the time series: xₜ= β₁+ β₂t + wₜwhere β1 and β2 are known constants and wₜ is a white noise process with variance σ ²_w.(a) determine whether xₜ is stationary.(b) show that the process yₜ= xₜ − xₜ₋₁ is stationary.(c) show that the mean of the moving averagevt = [1 /2q + 1] (j=-q→q) σ xₜ₋ⱼis β₁ + β₂t, and give a simplified expression for the autocovariance function.

Afarmer has a large field that is x feet in length. he wants to fence in a rectangular section in the middle of the field , leaving a length of 100 feet of open field behind each end of the fenced rectangle.he also wants the width of the fenced-in space to be 100 feet less than its length. find the expressions to represent the length and width of the fenced section of the field

Assume that adults have iq scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. find the probability that a randomly selected adult has an iq between 80 and 120.assume that adults have iq scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. find the probability that a randomly selected adult has an iq between 80 and 120.

|z| > (1/2) {-1/2, 1/2} {z|(-1/2) < z < (1/2)} {z|z < (-1/2) ∪ z > (1/2)}