Calculate a Random Sum

Calculator for a random sum, where with every step a random value from a given range is added. The start is 0. A random number is determined, to this another random number is added, and so on. Please enter the number of steps and the range of the random numbers. The results will be shown in a table. The calculation is an iteration of the form z=z+r, where r is the random value. However, the iteration calculator does not allow random numbers.

In the preset sequence, a value between -10 and +10 is added or subtracted 100 times, or a value between 0 and 10 is added or subtracted. These mean the same thing. In probability theory, the average value added each step is called an expected value, which here is 0. So, on average, nothing is added at each step, meaning the value doesn't change. Nevertheless, the values ​​do change because the actual added values ​​can and do deviate from the average. On average, 0 is also expected for the final result. This is the expected value for the outcome. In practice, however, a very large number of trials will be necessary to actually achieve 0. The final results are roughly as often negative as positive and are usually in the double digits.

If only positive values ​​are used for the random number range, the resulting function curve is called the Devil's Staircase, a singular function that is monotonically increasing, continuous, and nowhere differentiable. Its name comes from its resemblance to a staircase with steps of varying heights. This type of function can be visualized using the function graphs plotter, for example, with the function expression y(0)+rand(0#10)/100. The preset function can be simulated with the expression y(0)+rand(-10#10)/100.