Impact of Sample Size on Approximating the Uniform Distribution

This Mathematica demonstration compares the sample uniform probability distribution with the theoretical distribution. Probability and statistical theory shows us that as the number of samples increases for the given parameter values, the more closely the sample probability distribution will resemble the theoretical distribution. You can verify this by specifying the minimum and maximum parameter values that describe a sample uniform probability distribution. The specified number of samples is randomly generated from the uniform distribution and compared to the theoretical distribution. Users can select the minimum and maximum parameter values for the uniform distribution. By definition, the minimum is less than the maximum. The sample probability distribution is compared to the theoretical uniform distribution as you increase the sample size. In general, as the sample size increases, the more closely the sample distribution matches the theoretical distribution. The red dot shows the mean value for the theoretical distribution. The blue dot shows the mean value for the sampled distribution—they overlap when the distributions are close