# Exercise Solution 5.1

- 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).

- 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).

- 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.