# 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

## 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:

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

## Resources

### First Lecture

Slides | Videos |
---|---|

Slides | Video 001 Video 002 |

### Second Lecture

Lab | Videos |
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Lab | Video 001 Video 002 |