3-1. Why Probability

Sources of Uncertainty

1. Inherent Stochasticity in system being modeled
2. Incomplete observability
3. Incomplete modeling

3-2. Random Variables

• A variable that can take on different values randomly
• A mapping function from outcomes in sample space to a measurable space

3-3. Probability Distributions

Probability distribution

→ A description of how likely a random variable or a set of random variables is to take on each of its possible states

3-3-1. Discrete Variables and Probability Mass Function

Probability mass function(PMF)

→ PMF maps from a state of a random variable to the probability of that random variable taking on that state

→ A probability distribution over discrete variables may be described using a PMF

Axioms of a PMF

1. domain of $P$ must be the set of all possible states of $x$