normal random variable is a continuous random variable that allows you to manually specify the expectation and variance

constituents

• \(\mu\) the mean
• \(\sigma\) the variance

requirements

\begin{equation} X \sim \mathcal{N}(\mu, \sigma^{2}) \end{equation}

PDF:

\begin{equation} f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} \end{equation}

additional information

normal maximizes entropy

no other random variable uses as little parameters to convey as much information

Use a series of parametrized differentiable + invertible functions to transform simple distributions to complex ones.

Foreword

Hi there, internet traveler.

The time is 2015/2016, I was either in 5th or 6th grade. At that time, I was barely beginning to be actually comfortable using the language of English.

One of the ways I practiced English, which is also a habit I continue to do today, is to write. I write mostly expository prose now, but, back then, shining with childish naïvete, I decided to write a multi-part story as a means of practicing English.

\(\text{NP} \cap \text{coNP}: \forall x \in \qty {0,1}^{*}, \exists\) short, efficiently checkable proof of BOTH \(x\) presence/absence in \(L\)

some examples

• in P: PERFECT-MATCHING
• in P: PRIMES
• we don’t know if this is in \(P\): FACTORING … if it was, much of cryptography will break

“Doing NSM analysis is a demanding process and there is no mechanical procedure for it. Published explications have often been through a dozen or more iterations over several months” — (Heine, Narrog, and Goddard 2015)

Approach and XD

Introduction and Theory

The Natural Semantic Metalanguage (NSM) approach (Wierzbicka 1974) is a long-standing hypothetical theory in structural semantics which claims that all human languages share a common set of primitive lexical units—usually words, but, in some languages, short connected phrases—through which all other words in each language can be defined.