Birthday Experiment

Ball 1 Ball 2 Ball 3 Ball 4 Ball 5 Ball 6 Ball 7 Ball 8 Ball 9 Ball 10 Ball 11 Ball 12 Ball 13 Ball 14 Ball 15 Ball 16 Ball 17 Ball 18 Ball 19 Ball 20 Ball 21 Ball 22 Ball 23 Ball 24 Ball 25 Ball 26 Ball 27 Ball 28 Ball 29 Ball 30 Ball 31 Ball 32 Ball 33 Ball 34 Ball 35 Ball 36 Ball 37 Ball 38 Ball 39 Ball 40 Ball 41 Ball 42 Ball 43 Ball 44 Ball 45 Ball 46 Ball 47 Ball 48 Ball 49 Ball 50
Distribution graph

Description

The experiment is to draw a random sample of size \(n\) with replacement from a population of size \(m\). In the app, the population consists of \(m\) balls numbered from 1 to \(m\). The random variables of interest are \(V\), the number of distinct values in the sample, and \(I\), the indicator variable that indicates at least one duplication in the sample (the birthday event). On each update, the sample of balls is shown in the urn graph; a ball that duplicates a previously chosen ball is shown in red, and otherwise is shown in green. The values of \(V\) and \(I\) are recorded on each update in the data table. The probability density function of the selected variable is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density function of the selected variable is shown in red in the distribution graph and is recorded in the distribution table. The parameters \(m\) and \(n\) can be varied with scroll bars.