[career] Convert to JAX and content checks

[HumphreyYang]

This PR updates career by converting the code to JAX.

Some changes are done to vectorize the for loops in addition to some old change rules in the previous lectures.

For the exercise I left qe.random.draw function since there isn't much performance gain there!

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-617--sunny-cactus-210e3e.netlify.app (6232e18)

📚 Changed Lecture Pages: career

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-617--sunny-cactus-210e3e.netlify.app (1ededf4)

📚 Changed Lecture Pages: career

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-617--sunny-cactus-210e3e.netlify.app (5842d1e)

📚 Changed Lecture Pages: career

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-617--sunny-cactus-210e3e.netlify.app (8707aab)

📚 Changed Lecture Pages: career

[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-617--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 178 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 ~178 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-617--sunny-cactus-210e3e.netlify.app/career.html

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This PR touches: career.md. Last CI build: success@2025-09-18. Branch: 178 commits behind main as of 2026-07-08.