A description is given of an experiment to demonstrate the buildup of Poisson distributions with very high precision. Mean values up to 100 can be obtained, which enables a critical comparison of distributions with different means. By using small numbers of sampling periods, it is also possible to show how the means are themselves distributed, and to show that the standard deviation of the means is equal to σ/N1/2, where σ is the standard deviation of the ’’infinite’’ distribution andNis the number of sampling periods. Dead‐time effects are also investigated experimentally.