CS 445 - Expectation

Expectation, Variance

• Expectation (continuous) :

• Expectation (discrete):

• Variance:

Quiz

Imagine we are rolling a four-sided die. The probability distribution:

Questions:

• What is the expected value of this distribution?
• What is the variance?

Sample Mean and Variance

Expectation and variance are properties of distributions.
We can also calculate the sample mean and the sample variance for a dataset:

• Sample mean:

• Sample variance:

Normal Distribution

• "Normal" because of the central limit theorem