Sample Space S : set of all possible outcomes of conceptual/physical, repeatable experiment

Event A : any subset of S

Probability Theory:

1. Sample space is a collection of all possible outcomes
2. Random variables X represent outcomes in sample space
3. Probability of a random variable to happen $p(x) = p(X= x), p(x) ≥ 0$

Continuous variable:

$\int_{x}p(x)dx = 1$

• Continuous probability distribution
• Probability density function
• Density or likelihood value
• Temperature (real number)
• Gaussian Distribution

Continuous Probability Function examples

1. Uniform Density Function

$f_x(x) = \begin{cases}\frac{1}{b-a} \text{ for a ≤ x≤ b}, \\0 \text{ otherwise}\end{cases}$