## Random Walk Continous

The steps in a random walk can take on discrete or continuous values. Program `RandomWalkContinuous` allows you to explore how continuous random walks can be described in a similar way as walks with fixed steps as the number of steps $N \gg 1$.

**Problem: Simulation of a random walk with variable step length**

Use Program `RandomWalkContinuous` to simulate a random walk in one
dimension with a variable step length.

- The step length is generated at random with a uniform probability between 0 and 1. Calculate the mean displacement and its variance for one step.
- Compare your analytical results from part (a) to the results of your simulation for $N=1$ ($p=1/2$).
- How does the variance of the displacement found in the simulation for $N=16$ depend on the variance of the displacement for $N=1$ that you calculated in part (a)?
- Explore how the histogram changes with the bin width. What is a reasonable choice of the bin width for $N=100$?

## Resource

Problem 3.44 in*Statistical and Thermal Physics: With Computer Applications*, 2nd ed., Harvey Gould and Jan Tobochnik, Princeton University Press (2021).