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  • Random Variables

Discrete Random Variable

• Random variable can only take specific (finite or countably infinite) values.
• Expected Value
  • $\mu =E(X)=\sum X_i\cdot p(x_i)$
• Example:
  • Outcome of rolling a die once:
    • $\begin{array}{cccccc}1& 2& 3& 4& 5& 6\end{array}$
• The random variable cannot take any other value except for these specific ones.
  • Ex: can't get a die and get $2.3$
• Notation:
  • $P(X=x)=p(x)$
  • $x=$ actual value
  • $X=$ random variable
  • $p(x)=$ numeric probability of random variable being $x$
  • Support of a Random Variable