---
title: "Lecture 6 Note"
author: "Yiming Gong"
date: "2021-07-26T09:07:55Z"
link: "https://bookdown.org/yg484/lec_6_note/"
length_weight: "1.9%"
pinned: false
---

This is the class note for lecture 6. [...] Consider a data set of daily asset percent returns: \[
x_1, x2,\dots, x_n
\] Assume the return on day \(t\) is a random variable \(X_t\): \[
\{\text{all possible }X_t\} =\{-\infty <x_t<\infty\}
\] The probability model/distribution for \(X_t\) is given by specifying the cumulative distribution function or equivalently the probability density function Special Cases of the Probability Model in our exercise \[
f(x_t) = \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\frac{(x-\mu)^2}{\sigma^2}}
\] \[
f(x) = \frac{1}{2b}e^{-\frac{|x-\mu|}{b}}
\] Useful methods  ...
