prob_matrix.md: assorted corrections

[jstac]

A collection of issues found in lectures/prob_matrix.md, similar to those addressed in #877 / #878 for prob_meaning.md.

• Typos and grammar:
  • "Among concepts that we'll be studying include" → "Concepts that we'll study include" (line 22)
  • "underly" → "underlie" (line 75)
  • "a small number parameters" → "a small number of parameters" (line 284)
• IID terminology: Lines 134, 137, 1788 use "i.i.d." while line 167 uses both "IID" and "iid" in the same sentence. Standardize to IID for consistency with prob_meaning.
• PEP 8 naming: class discrete_bijoint: should be DiscreteBijoint (line 748). Verbose docstring style could also be trimmed.
• Replace prettytable with pandas: prettytable is used heavily throughout (lines 644–691, 748–857, 1327–1505). Replacing with pandas DataFrames would drop the dependency and render better in notebooks — same change made in Fix assorted issues in prob_meaning lecture #878 for prob_meaning.
• Plotting style: Commented-out # %matplotlib notebook magic commands on lines 956, 967 (dead code). Lines 972–973 mix plt.ylabel and ax.set_zlabel — should standardize to ax. methods.
• Unused import: from mpl_toolkits.mplot3d import Axes3D (line 58) is not needed since matplotlib 3.1+.
• Cross-reference: Line 1021 uses {doc}\this quantecon lecture <multivariate_normal>`` — should use the actual lecture title for better PDF rendering.
• {\rm Prob} vs \textrm{Prob} (line 149): One instance uses {\rm Prob} while the rest of the lecture uses \textrm{Prob}. Should be consistent.
• Braces vs parentheses for Prob: Lines 104, 110, 210 use \textrm{Prob}(...) with parentheses, but most other lines use \textrm{Prob}\{...\} with braces. Should pick one convention. Note that prob_meaning uses parentheses throughout.
• Variance operator: Lines 579, 588, 1050 use $\mathbb{D}[X]$ for variance, which is uncommon. The exercises (line 1694) already use $\text{Var}(Z)$, creating an inconsistency. Standardize to $\mathbb{V}[X]$.
• $\mathrm{E}$ vs $\mathbb{E}$ (line 588): One instance uses \mathrm{E} while the rest of the lecture uses \mathbb{E}. Should be \mathbb{E} consistently.
• Normal distribution notation: Lines 1015–1016 use $\mathbb{N}[...]$ with blackboard bold and square brackets. Should be $N(\mu, \sigma^2)$ with plain $N$ and parentheses.
• Cross-lecture density notation: prob_meaning uses $p(\theta)$ for density while prob_matrix uses $f(x)$. Using $f$ for densities is standard but readers encounter $p$ first in the TOC ordering. Worth noting for future consistency passes.
• Ill-defined integral (lines 107–111): The equation $\textrm{Prob}(X \in A) = \int_{\mathcal{G}} p(\omega), d\omega$ assumes $\Omega \subseteq \mathbb{R}^n$ with Lebesgue measure, but $\Omega$ was introduced as an abstract set of outcomes. Either qualify (e.g., "If $\Omega \subseteq \mathbb{R}^n$ and $\mu$ has a density with respect to Lebesgue measure...") or introduce a dominating measure.

[jstac]

Note: If QuantEcon/QuantEcon.manual#84 is merged (which standardizes on \mathbb{P} for probability notation), the \textrm{Prob} / {\rm Prob} items in this issue should be resolved by switching to \mathbb{P}\{...\} throughout. Same applies to \mathbb{E}, \mathbb{V}, plain $N$ for normal, and the other conventions proposed there.

[nightcityblade]

Hi, I'd like to work on this. I'll submit a PR shortly.