First vectorized approach in intro is incorrect algorithm.

[BoydstonNicholas]

So I started reading the book and have gotten to the introduction so far (section 2.1). I noted a couple of issues and thought "I can help!...kinda".

The first vectorized approach to the random walk, which used the code steps = random.sample([1, -1]*n, n) does not in fact produce a random walk.

This is because the random.sample() function performs sampling without replacement. All other random walk definitions I have seen, including the rest of the ones in the introduction, perform their sampling with replacement.

In order to bring this implementation into line with the others in the introduction I might suggest using the random.choices() function.

steps = random.choices([1,-1], k=n)

I also noticed a minor notational issue that could use some clarification. I believe that many people would refer to the "Functional approach" as a "Procedural approach". The word "Functional" is sometimes reserved for the functional programming style which makes heavy use of higher order functions. I cannot say, however, how universal such terminology is.

Looking forward to reading onward.

[rougier]

Thanks, I didn't noticed sample was doing sampling without replacement. I'll change in favor of your solution which is also more readable. But in this specific case, taking n samples among 2n samples (having only 2 different values), would that make a statistical difference ?

I'll also correct the Functional approach since the term is ambiguous as you underlined.

Thanks again.

[BoydstonNicholas]

Cool. Glad to be able to help.
I'm pretty sure it does make a statistical difference, because it would tend to stay more balanced. That is, if a bunch of -1s had already been chosen the next choice would be more likely to be a +1 because there would be more +1s left.