Suppose xt = m + wt + qwt1, where wt ? wn(0, s2w ). (a) Show that mean function is E(xt) = m. (b) Show that the autocovariance function of xt is given by gx(0) = s2w (1 + q2), gx(?1) = s2w q, and gx(h) = 0 otherwise.(c) Show that xt is stationary for all values of q 2 R.(d) Use (2.20) to calculate var( ¯ x) for estimating m when (i) q = 1, (ii) q = 0, and (iii) q = 1 (e) In time series, the sample size n is typically large, so that (n1) n ?1. With this as a consideration, comment on the results of part (d); in particular, how does the accuracy in the estimate of the mean m change for the three different cases?

Iwill mark brainliest worth 30 pointsthe distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph: a graph titled motion of ant is shown. the graph shows time in seconds on the x-axis and the distance from hole in centimeters on the y-axis. the scale on the x-axis is shown from 0 to 6 at increments of 1, and the scale on the y-axis is shown from 0 to 12 at increments of 2. the graph has 3 straight lines. the first line is labeled p and joins ordered pairs 0, 0 and 2, 6. the second line is labeled q and joins ordered pairs 2, 6 and 3, 6. the third line is labeled r and joins ordered pairs 3, 6 and 5, 0.part a: is the graph linear or nonlinear? explain your answer. (2 points)part b: in which segments is the graph increasing, decreasing, and constant? (3 points)part c: in your own words, describe the motion of the ant, as shown on the graph. (5 points)