stock market crash of 1929

At October 24th, 1929, Black Thursday took place, and the stock market crashed. During this time, a record of 13 million shares traded, over $3b of losses. This began a 4 year slide of the global economy.

Crash theories:

• demand-driven theory
• Monetarist theory

bank failures of 1929

Banks became irrelevant. Lots of risky loans given out, farmers are taken out huge loans and the banks can’t deal.

“If sample size is large and IID, the sampling distribution is normal. The larger \(N\) is, the more normal the resulting shape is.”

We can use the central limit theorem to estimate the sum of IID random variables:

Let there be \(n\) random variables named \(X_{j}\), they are IID, and they have \(E[x] = \mu\), and \(Var(x) = \sigma^{2}\)

We have that:

\begin{equation} \sum_{i=1}^{N} X_{n} \sim N(n\mu, n \sigma^{2}), \text{as}\ n \to \infty \end{equation}

That, as long as you normalize a random variable and have enough of it, you get closer and closer to the normal distribution.

A language \(A\) is in \(NL\) if \(\exists\) a deterministic Turing Machine \(V\) that runs in logspace where \(x \in A \Leftrightarrow \exists w \in \qty {0,1}^{\text{poly}\qty(|x|)}\) (if and only if!! same as NP) such that \(V \qty(x,w) = 1\), where $x$—the real input \(x\) is on input tape one which is read-only, and the witness \(w\) is on input tape two which is read-once (because otherwise the same definition is equivalent to \(NP\)).