Axioms of Probability

This then leads to further rules

Conditional Probability

Uniform Distribution

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