Probability and Random Variables Review

• Random Variable: A variable that takes on its values by chance.
• Discrete RV: Takes on a finite or countable set of values. Described by Probability Mass Function (PMF) $p(x)=P\{X=x\}$.
• Continuous RV: Takes on a continuum of values. Described by Probability Density Function (PDF) $f(x)$ where $P\{a\le X\le b\}={\int }_a^{b}f(x)dx$.
• Distribution Function (CDF): $F(x)=P\{X\le x\}$.
• Mean (Expectation): $E[X]=\sum xp(x)$ or $\int xf(x)dx$.
• Variance: $Var[X]=E[X^2]-(E[X]{)}^2$.