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

[Chihiro2000GitHub]

Summary

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

The single np.random.randn(...) draw is replaced with an explicit rng = np.random.default_rng(), threaded through the simulation functions.

Related PRs and issues

I checked for open PRs and issues related to this lecture. No open PR touches it and no open issue concerns it — nothing overlaps with this migration.

Details

• rng = np.random.default_rng() is defined once in the imports cell (main text).
• np.random.randn(m) → rng.standard_normal(m).
• rng is passed explicitly as an argument through simulate_var and simulate_samuelson, and all call sites are updated. The lecture has no @jit/prange code, so rng can be threaded as an ordinary argument.
• No fixed seed is introduced, since the lecture did not seed before.

mvn.rvs (scipy). simulate_var also draws the initial state via scipy.stats.multivariate_normal.rvs, which otherwise uses NumPy's global random state. To keep the whole function on the single explicit generator, I pass random_state=rng — supported per the scipy manual, whose random_state/seed accepts a numpy.random.Generator. This is slightly beyond the pure np.random scope; if you'd prefer to leave mvn.rvs untouched, just say so and I'll revert that one line.

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

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