Using statistics for Siletz River peak flows, 1979-1999 (Table 3-1), generate a series of normally distributed synthetic

Question:

Using statistics for Siletz River peak flows, 1979-1999 (Table 3-1), generate a series of normally distributed synthetic stream flows by following these guidelines.
(a) By performing a regression of flows for the period 1980-1999 vs. flows during 1979¬1998, verify that the serial correlation coefficient for this time period is 0.1411.
(b) Verify that the mean and unbiased standard deviation for the full 21 -year period are 19,343 cfs and 7217 cfs, respectively. Use these values for part (c).
(c) The list of 21 N (0,1) random numbers below was generated in Excel using the Tools/Data Analysis/Random Number Generation option with a seed of 12345. (The option for a seed allows one to generate identical sequences of random numbers.) Assuming that the initial flow mean (at "step 0"), generate a sequence of 21 random flows using Eq. (3-83). Compute the mean, standard deviation, and serial correlation coefficient of the synthetic flow sequence to see how well these statistics are preserved. Optional: Create a new series of N (0,1) random numbers and repeat the generation. Notice that as the mean and standard deviation of the random numbers differ from 0 and 1, respectively, so do the mean and standard deviation of the synthetic sequence differ from their historic values.