Use a runs test and calculate auto relations to decide whether the random series explained in each part of this problem (a–c) are random. For each part, generate at least 100 random numbers in the series.
a. A series of independent normally distributed values, each with mean 70 and standard deviation 5.
b. A series where the first value is normally distributed with mean 70 and standard deviation 5, and each succeeding value is normally distributed with mean equal to the previous value and standard deviation 5.
c. A series where the first value, Y1, is normally distributed with mean 70 and standard deviation
5, and each succeeding value, Yt, is normally distributed with mean (1 + at)Yt - 1 and standard deviation 5(1 + at), where the at values are independent and normally distributed with mean 0 and standard deviation 0.2.