[officialasishkumar]

Fixes #1111

Four small fixes from the review in #1111:

• back_prop: train split key each epoch but drew the permutation from a fixed random.key(1), so the data came in the same order every epoch. It now draws from the fresh subkey.
• stats_examples: the negative binomial mean and variance now use the parameter r instead of k: $\mathbb{E}(X) = r(1-p)/p$, $\mathbb{V}(X) = r(1-p)/p^2$.
• endogenous_lake: the text accepts an offer when $w \geq \bar w$, but the code counted w_vec > w_bar, understating the job finding rate by $\gamma,p(\bar w)$. Changed to >= in the three places listed in the issue, and fixed the "paramters" typo in the printed message.
• multi_hyper: count now takes its loop length from vec1.shape[0] instead of the global sample, which Numba freezes at compile time.

I did not rebuild the lectures locally (no JAX/Numba environment on the machine I used); the changes are one-line edits matching the descriptions in the issue.