[monte_carlo.md] Update np.random → Generator API

[Chihiro2000GitHub]

Summary

This PR migrates legacy NumPy random API usage in monte_carlo.md as part of QuantEcon/meta#299.

• Replaced from numpy.random import randn with rng = np.random.default_rng() in the imports block.
• Replaced all randn(), randn(n), np.random.randn(M), and np.random.randn(2, M) calls with the corresponding Generator API methods (rng.standard_normal()).

Details

rng is defined once at module level in the imports block and reused throughout the lecture, including in the exercise solution blocks. In previous lectures, exercise solution blocks were typically treated as self-contained and rng was redefined within each solution block. In this lecture, however, the exercise solutions were already not self-contained — they relied on the module-level randn import rather than defining their own random source — so defining rng at module level and reusing it throughout is the more natural and consistent pattern here.

No fixed seed was introduced. No Numba-related code was present.

Hi @mmcky and @HumphreyYang, I'd be grateful if you could take a look when you have time.

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[HumphreyYang]

Many thanks @Chihiro2000GitHub! It looks nice. Just one comment:

In this PR, a number of functions rely on the global rng object.

In some other PRs, rng is passed in as an argument instead. I think that approach is preferable here because it makes the source of randomness explicit and avoids hidden global state, which should make the functions easier to test and reason about.

So it would be nice to make a few minor edits so that these functions accept rng as an argument.

[Chihiro2000GitHub]

Thank you for the feedback, @HumphreyYang! I've updated all functions in monte_carlo.md to accept rng as an explicit argument with rng=None as the default, following the pattern used in other PRs. Each function now creates its own generator via np.random.default_rng() if none is provided, and all call sites in the lecture have been updated to pass rng=rng explicitly.

[HumphreyYang]

Many thanks, @Chihiro2000GitHub!

It is nice that you have this:

if rng is None:
    rng = np.random.default_rng(

which is important for a mature Python program.

However, I think that for here, since we are always going to pass an rng to the function, we can safely do what you did in:

PR #874 in lecture-python.myst

and remove this repetitive rng check for simplicity.

It's important that edits across PRs are using the same convention.

What do you think?

Also just one more small comment on a line that exceeds 80 characters.

[HumphreyYang]

This line is over 80 characters.

[jstac]

many thanks for the nice review @HumphreyYang .

@Chihiro2000GitHub , please address those review comments when you have time.

[Chihiro2000GitHub]

Thank you for the suggestion, @HumphreyYang!

I've removed the if rng is None guard from all functions and reformatted the simulate_asset_price_path signature to one-argument-per-line style.

For the default value, I've used rng=rng (referencing the global rng defined at the top of the notebook) rather than no default. The reason is a Python syntax constraint: since the other parameters already have defaults (e.g. n=default_n), a bare rng with no default would need to come before them or be written as *, rng (keyword-only) — see Python docs on compound statements. I wanted to keep the argument order intact and avoid introducing *, so rng=rng seemed like the simplest viable option.

That said, I'm happy to adjust. Would you prefer *, rng (required keyword-only argument) or moving rng to the first position instead?

Thanks also for the reminder, @jstac!

[jstac]

thanks @Chihiro2000GitHub @HumphreyYang . merging