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

[Chihiro2000GitHub]

Summary

This PR migrates legacy NumPy random API calls in numpy.md as part of QuantEcon/meta#299.
All np.random.randn, np.random.binomial, and from numpy.random import uniform usages are replaced with the Generator API via np.random.default_rng().

Details

• rng = np.random.default_rng() is introduced at the first point of use (Mutability section) and reused throughout the main lecture text.
• Exercise solution blocks (np_ex3, np_ex4) define their own local rng to remain self-contained.
• np_ex4 (Part 1 and Part 2, exercise and solution) retains seed 123 via np.random.default_rng(123), matching the original intent of reproducible comparison between broadcasting and for-loop results.
• DiscreteRV in the np_ex2 solution stores self.rng = np.random.default_rng() in __init__ and uses self.rng.uniform(...) in draw.
• No fixed seed was introduced beyond what was already present in the original.
• No Numba-related code was found in this file.
• Local build completed successfully (jb build lectures); numpy.md executed without errors in 30 seconds.

Notes for reviewers

One item was intentionally left unchanged and would benefit from reviewer judgment:

The prose in the Sub-packages section currently reads:

We've already seen how we can generate random variables using np.random

After this migration, the code directly below uses rng.standard_normal() and rng.binomial() rather than np.random.xxx() directly. Technically rng is still obtained from np.random.default_rng(), so the sentence is not wrong — but it may feel slightly mismatched to a reader. Happy to update the wording if you think that would be clearer.

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

[github-actions]

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[HumphreyYang]

Hi @Chihiro2000GitHub,

This looks great to me! The only small suggestion I have is that

We’ve already seen how we can generate random variables using `np.random`

seems a bit stale because we are specifically using the Generator API. I think

We've already seen how we can generate random variables using NumPy's Generator API.

would be a better description.

Another minor point is that we can potentially allow for the seed key to be passed for the exercise solution by:

class DiscreteRV:

    def __init__(self, q, seed=None):
        self.q = q
        self.Q = cumsum(q)
        self.rng = np.random.default_rng(seed)

    def draw(self, k=1):
        return self.Q.searchsorted(self.rng.uniform(0, 1, size=k))

Please let me know what you think!

[Chihiro2000GitHub]

Hi @HumphreyYang,

Thank you for the feedback! Both of your points make perfect sense.

I've addressed both points:

1. Updated the prose from np.random to "NumPy's Generator API" to better reflect the current usage.
2. Added an optional seed parameter to DiscreteRV.__init__.

Please let me know if anything else needs adjusting!