New lecture: split out "Samples vs Distributions" from prob_dist

[jstac]

Proposal

Pull everything from the "Observed distributions" section onwards out of prob_dist.md and make it a separate lecture titled "Samples vs Distributions" that treats the relationship between samples and distributions more carefully than the current brief treatment.

Motivation

prob_dist.md is currently doing two jobs: (1) introducing probability distributions and common families, and (2) working with observed data. Splitting the second job into its own lecture lets each breathe, and gives us room to develop the sample↔distribution connection properly — which is currently quite compressed.

Scope of the new lecture

Expanding on what's already in the "Observed distributions" section, the new lecture would cover:

• Sample moments — the sample mean and other sample moments (variance, higher moments).
• Visualizing samples — histograms, empirical CDFs (ECDFs), kernel density estimates (KDEs), violin plots, and box-and-whisker plots.
• Convergence — show that sample-based estimates of a distribution converge to the true distribution / density as the sample size grows (e.g. ECDF → CDF, histogram/KDE → density, sample moments → population moments).
• The role of independence — flag the crucial role that independence of the observations plays in this convergence.

Notes

• The current "Observed distributions" content (income example, summary stats, histograms, KDEs, violin plots, and the "connection to probability distributions" normal-fit material) is the natural seed for the new lecture.
• Will need a _toc.yml entry and cross-references from prob_dist (and vice versa).
• Related: the new height example in prob_dist (PR prob_dist: motivating height example and Japan age distribution #790) already previews the "fit a distribution to data" idea, which this lecture would develop.

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