Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Random Experiment

Let's have a look at a fairly simple, precisely defined experiment, which was originally performed to investigate the laws of gravitation. A steel ball is mounted at some known fixed height above ground within an evacuated apparatus. When the steel ball is released, the time until it hits the ground plate is measured. Suppose the steel ball is mounted at a height of exactly 5 meters above ground. Using an electronic stopwatch with a time resolution of 0.001 sec, we would determine that the steel ball needs 1.010 seconds to hit the ground. Now let's repeat the experiment. Again, the steel ball needs 1.010 seconds to hit the ground. Repeating the experiment 10 times, we find the following free fall durations (in seconds):

1.010, 1.010, 1.010, 1.010, 1.010, 1.010, 1.010, 1.010, 1.010, 1.010

Now let's conduct the same investigation once again, but replace the electronic stopwatch with a device which has a 10 million fold time resolution (nsec instead of msec). Repeating the experiment 10 more times, we now find the following values for the duration of the free fall:

1.009810350, 1.009810943, 1.009810257, 1.009810072, 1.009810929,
1.009810704, 1.009810009, 1.009810542, 1.009812001, 1.009800763

Looking at the outcome of the second set-up, we see that the results are exact only to a certain precision. Increasing the precision of the experiment finally reveals some fluctuations in the results which seam to be completely random. When we use some kind of  "magnification glass" to look at the results, we finally find that the outcome varies from time to time. You may go to the  DataLab  to have a look at the data.

The result of this experiment can be seen in more fundamental way:

Any experiment producing an analog signal will finally show up
random numbers if we only measure the results precisely enough.

Last Update: 2012-10-08