Expectation

An expectation of value $E(X)$ means the expectation or average of a given Random Variable Probability has everything to do with expectations. Thought of as the weighted center of a Probability Distribution.

Properties

• Linearity $E(aX+bY+c)=aE(X)+bE(Y)+c$
• Expectation of constant is constant $E(c)=c$
• Expectation once calculated is a constant $E(E(X))=E(X)$
• Independent $X\perp Y⟹E(XY)=E(X)E(Y)$
• $E(X-E(X))=0,\forall X$

Concepts

• Expectation as the Center of a Circle
• Expected Value of Discrete RV
• Expected Value of Function
• Expected Value of Indicator RV
• Expected Value of Continuous RV
• Expected Value of Discrete Multiple RV
• Expected Value of Continuous Multiple RV
• Fair Game
• Expected Value Example
• Conditional Expectation