There are many condition in the Great Depression caused

• by 1932, 1/4 had no work
• emigration exceeded immigration
• decrease in American birth
• increase of mental illness and suicide
• people create Hooverviles
• movies and radio became much more popular

proportional confidence intervals

We will measure a single stastistic from a large population, and call it the point estimate. This is usually denoted as \(\hat{p}\).

Given a proportion \(\hat{p}\) (“95% of sample), the range which would possibly contain it as part of its \(2\sigma\) range is the \(95\%\) confidence interval.

Therefore, given a \(\hat{p}\) the plausible interval for its confidence is:

\begin{equation} \hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \end{equation}

where, \(n\) is the sample size, \(\hat{p}\) is the point estimate, and \(z*=1.96\) is the critical value, the z-score denoting \(95\%\) confidence (or any other desired confidence level).

Could a different choice of evaluation order change the terminating result of the program; note that this says nothing about whether or not particular evaluation order terminates.

constituents

requirements

A set of rewrite rules is confluent if for any expression \(E_0\), should \(E_0 \to^{* } E_1\) and \(E_0 \to^{* } E_2\), then there exists some \(E_3\) such that \(E_1 \to^{*} E_3\) and \(E_2 \to^{ *} E_3\)

Why this instead of saying we will end up at one state after all evaluations? Suppose a particular system never terminates, we have to specify a particular confluent state because otherwise the notion of all is bad.

A conjugate prior of a certain likelihood function \(p\qty(x | \theta)\) is a type of prior where the posterior distribution—

\begin{equation} p\qty(\theta | x) \end{equation}

is the same probability family as the prior \(p\qty(\theta)\).

This means that updating is very easy; if we can’t do this, probabilistic programming!

conjugation is the process of building a similar matricies.