Exercise Solution 5.1

1. Many empirical tests might be considered. Let’s consider the following five:
   • sample mean,
   • sample standard deviation,
   • sample autocorrelation (lag 1),
   • sample autocorrelation (lag 2),
   • sample autocorrelation (lag 3).
2. Results obtained using a spreadsheet are indicated below (results in parenthesis indicate what would be expected for pseudorandom numbers).
   • sample mean: .496 (.500),
   • sample standard deviation: .285 (.289),
   • sample autocorrelation (lag 1): .019 (.000),
   • sample autocorrelation (lag 2): .552 (.000),
   • sample autocorrelation (lag 3): .100 (.000).
3. While 40 is a very small sample size, we still may consider the numbers not pseudorandom based upon the large sample autocorrelation for lag 2.