Week 4
This week, we will discuss Expected Values and Moment Generating Function.
Learning Outcomes
First Lecture
Moment Generating Functions
Expected Value Properties
Second Lecture
- Expected Values
- MGF
Lecture
Videos
| Section | Tuesday | Thursday |
|---|---|---|
| 001 | Video | Video |
| 002 | Video | Video |
Important Concepts
First Lecture
Moments
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:
\[ E(X^k)=\frac{d^km(t)}{dt}\Bigg|_{t=0} \]