# Axioms of Probability

This then leads to further rules

# Conditional Probability

# Independent Probabilities

## Pairwise Independence

Every pair of events are independent of each other

## Mutual Independence

The probability of all of a subset of events happening in the multiplication

# Random variable

The probability that a variable takes a certain value

## Independence

The probability $A=x$ and $B=y$ is the probability $A=x$ multiplied by the probability $B=y$

## Expected value

The expected value is x times the probability of x for all x

This can also be shown as the area under the curve

## Linearity of expectation

The expected value of A and B is the expected value of A plus the expected value of B

**This doesn’t apply for multiplication, only if they are independent**