[hoist_failure] Clean up the code and correct minor errors

[HumphreyYang]

This PR cleans up the code and correct minor errors and typos across the lecture.

It also improves the printing and smooth some of the sentences.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-656--sunny-cactus-210e3e.netlify.app (a9df52c)

📚 Changed Lecture Pages: hoist_failure

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-656--sunny-cactus-210e3e.netlify.app (174da1f)

📚 Changed Lecture Pages: hoist_failure

[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: https://pr-656--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 166 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Recommended first step for this PR

Update this branch to main (merge or rebase — pulls in #939 plus ~166 other commits), then let CI rebuild. On today's latest libraries the site builds clean, so the preview should return. house_auction is the known blocker; updating also picks up other since-merged fixes — rebuild and address any remaining per-lecture failures. Verify with:

curl -sI https://pr-656--sunny-cactus-210e3e.netlify.app/hoist_failure.html

---

This PR touches: hoist_failure.md. Last CI build: success@2025-11-14. Branch: 166 commits behind main as of 2026-07-08.

[Chihiro2000GitHub]

Hi @HumphreyYang, I'm working through the NumPy random API migration in QuantEcon/meta#299, and hoist_failure.md is one of the lectures still on the list.

This PR already rewrites the sampling cell, so rather than open a separate PR that changes the same lines, I thought I would ask here first. While you are in there, would you be happy to use the Generator API for those draws?

rng = np.random.default_rng(1234)
s1 = rng.lognormal(μ, σ, n_samples)
s2 = rng.lognormal(μ, σ, n_samples)
s3 = rng.lognormal(μ, σ, n_samples)

That keeps the seed you added, and it saves us both from a conflict on the same lines.

If you would rather keep this PR as it is, I am happy to do the migration in a separate PR once this one is merged.

[jstac]

Thanks @Chihiro2000GitHub, and sorry for the slow reply — @HumphreyYang hasn't been able to get back to this one, so I've picked it up.

Yes, let's do it here rather than in a separate PR. I've made exactly the change you suggested on this branch:

rng = np.random.default_rng(1234)
s1 = rng.lognormal(μ, σ, n_samples)
s2 = rng.lognormal(μ, σ, n_samples)
s3 = rng.lognormal(μ, σ, n_samples)

It replaces the np.random.seed(1234) plus legacy np.random.lognormal that this branch had introduced, and keeps the seed. That's the only sampling in the lecture, so hoist_failure.md should be clear for meta#299 once this merges — worth ticking off your list rather than opening a follow-up.

Asking first was the right call: this branch rewrites that cell substantially, so a parallel PR would have conflicted on exactly those lines.

While updating the branch I also merged current main into it (it was 218 commits behind, which was why the preview was 404ing), added the mystnb captions the figures style guide asks for, and brought the install cell into line with the other cells. The figures will shift slightly because PCG64 draws a different stream from the legacy RandomState — shape and magnitude are unchanged, which is the expected outcome noted in the migration guidance.

[jstac]

Opened #1027 for the two new exercises — exercise 2 can't be answered as posed (the comparison it asks for holds by linearity of expectation regardless of the rare event approximation), and exercise 1's conclusion of $p = 13$ disagrees with the $p = 15$ used in the lecture body. Neither is a regression against main, so this PR needn't be blocked on them.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-656--sunny-cactus-210e3e.netlify.app

Commit: e717c0a

📚 Changed Lectures

• hoist_failure

---

Build Info

• Workflow: Build Project [using jupyter-book]

[Chihiro2000GitHub]

Thank you @jstac for picking this up!

I really appreciate you making the change I suggested -- that's very helpful. I've noted this in QuantEcon/meta#299.

Thanks again!