The variance of a time series governed by the AR(1) model with f = 0.8, is 25. Compute the variances of the sampling distributions of averages of consecutive values of this time series, with lengths...

The variance of a time series governed by the AR(1) model with f = 0.8, is 25. Compute the variances of the sampling distributions of averages of consecutive values of this time series, with lengths

a. n = 5

b. n = 10

c. n = 50

For the temperature data in Table 9.7,

a. Calculate the first two harmonics.

b. Plot each of the two harmonics separately.

c. Plot the function representing the annual cycle defined by the first two harmonics. Also include the original data points in this plot and visually compare the goodness of fit.