AS/A2 Stats 2 Stats 3

S1 Topic 3: Probability
The birthdays experiment - extended
The birthday experiment is to draw a random sample of size n with replacement from a population of size N. In the applet, the population consists of N balls numbered from 1 to N. We are interested in the event that there is at least one duplication in the sample; the indicator variable of this event is denoted I. On each update, the sample of balls is shown in the first graph; a ball that duplicates a previously chosen ball is shown in red, and otherwise is shown in green. The value of I is recorded on each update in the first table. The discrete probability density function of I is shown in blue in the second graph and is recorded in the second table. On each update, the empirical probability density function of I is shown in red in the second graph and is recorded in the second table. The parameters N and n can be varied with scroll bars.

an applet from the Virtual Laboratories in Probability and Statistics