For the equatorial noontime temperature sequence xn of

Question

For the equatorial noontime temperature sequence Xn of Problem 10.4.1, a second sequence of averaged temperatures is W_n = [X_n + X_n-1]/2. Is W_n an iid random sequence?

Problem 10.4

Suppose that at the equator, we can model the noontime temperature in degrees Celsius, X_n, on day n by a sequence of iid Gaussian random variables with a mean of 30 degrees and standard deviation of 5 degrees. A new random process Y_k = [X_2k-1 + X_2k]/2 is obtained by averaging the temperature over two days. Is Y_k an iid random sequence?