“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 \(NP\)).