A random walk¹ is a random process in which a state at time t is only dependent on the state at time t-1. Let us take a look at the following process:

$$X_t=X_{t-1}+N(0,{\sigma }^2)$$

with $N(0,{\sigma }^2)$ being a normal distribution with mean 0 and variance ${\sigma }^2$.

Simulate a random walk of 100 steps using the standard normal distribution (i.e. with ${\sigma }^2=1$):

• Generate 100 random variates from a standard normal distribution using the function rnorm(). Store them in a vector called random_vals.
• Use random_vals to create a simple random walk based on the formula above. Store that in a vector called random_walk.

In order to validate your (random) results, we set a seed for R’s random number generator, which you can leave as is.