doc: clarity revisions added neg-bin example

[bbbruce]

Made revisions that helped me understand better and completed the negative binomial example adding a combo negative binomial and face mask time scaling example.

[dinacmistry]

Suggested change

	- **Cumulative Distribution Function (CDF)**: A function giving the probability that a random variable is less than or equal to a specific value. For a continuous r.v. with PDF $`f_X`$, $`F_X(x) := P(X \leq x) = \int_{-\infty}^x f_X(w) dw`$.
	- **Cumulative Distribution Function (CDF)**: A function giving the probability that a random variable is less than or equal to a specific value. For a continuous random variable with PDF $`f_X`$, $`F_X(x) := P(X \leq x) = \int_{-\infty}^x f_X(w) dw`$.

[dinacmistry]

Suggested change

	- **Exponential Distribution**: A continuous probability distribution describing the time between events in a Poisson process, with PDF $`f(x) = \lambda e^{-\lambda x}`$ for $`x \geq 0`$. If an r.v. $`X`$ has exponential distribution with rate $`\lambda`$, we write $`X \sim \text{Exp}(\lambda)`$.
	- **Exponential Distribution**: A continuous probability distribution describing the time between events in a Poisson process, with PDF $`f(x) = \lambda e^{-\lambda x}`$ for $`x \geq 0`$. If an random variable $`X`$ has exponential distribution with rate $`\lambda`$, we write $`X \sim \text{Exp}(\lambda)`$.

[dinacmistry]

Suggested change

	- The distribution of a positive continuously distributed random variable $`X`$ is **memoryless** if $`P(X>t) = P(X > s+t \mid X > s)`$ for all $`s, t\geq 0`$.

[dinacmistry]

Suggested change

	**Lemma:** The distribution of a positive continuously distributed random variable $`X`$ is memoryless iff $`P(0\lt X \lt t) = P(s\lt X \lt t+s \mid X > s)`$.

[dinacmistry]

I'm working on a PR that makes edits to this one. For some reason that I can't recall now, I couldn't write to this branch (probably because it's from a fork). So hold off on any edits here or merging this please.