Week 4

This week, we will discuss Expected Values and Moment Generating Function.

February 10, 2023

Learning Outcomes

First Lecture

  • Moment Generating Functions

  • Expected Value Properties

Second Lecture

  • Expected Values
  • MGF

Important Concepts

First Lecture


The \(k\)th moment is defined as the expectation of the random variable, raised to the \(k\)th power, defined as \(E(X^k)\).

Moment Generating Functions

The moment generating functions is used to obtain the \(k\)th moment. The mgf is defined as

\[ m(t) = E(e^{tX}) \]

The \(k\)th moment can be obtained by taking the \(k\)th derivative of the mgf, with respect to \(t\), and setting \(t\) equal to 0:

\[ E(X^k)=\frac{d^km(t)}{dt}\Bigg|_{t=0} \]


First Lecture

Slides Videos
Slides Video 001 Video 002

Second Lecture

Lab Videos
Lab Video 001 Video 002