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

[Chihiro2000GitHub]

This PR updates legacy NumPy random API usage in python_by_example.md to the recommended Generator API.

I introduced a local rng = np.random.default_rng() and replaced the relevant legacy random calls using the new Generator API.

In the main lecture flow, I introduced rng only once and then reused it in subsequent cells, in order to keep the structure and presentation as close to the original as possible.

For the exercise solutions, I took a slightly different approach and introduced rng within each solution block. My reasoning was that these solutions seemed more natural as relatively self-contained answer units, especially since the exercise statements explicitly specify the relevant imports. That said, if this is not the preferred approach, it should be easy to revise by removing those local rng definitions.

I also updated the first sentence in Section 3.3.1.3 (“Subpackages”), since it explicitly referred to the legacy line np.random.randn(100) and would otherwise have become inconsistent with the revised code.

I built the lecture locally to check that the changes work as expected.

I’d be very glad to hear any thoughts, especially on the choice to define rng separately within each exercise solution block.

[github-actions]

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[HumphreyYang]

Many thanks, @Chihiro2000GitHub, and congratulations on your first QuantEcon PR!

This looks great to me. Your reasoning about redefining rng in solutions makes sense, and it would be nice to apply this rule consistently across lectures when making similar changes.

Just one minor suggestion: it would be helpful if you could reference the issue you are trying to resolve (or partially resolve, in this case):
QuantEcon/meta#299

Aside from that, this is a great PR!

Please feel free to move on to the rest of the lectures in the series. Also, remember to create a new branch based on main.