Problem: Conditional expectations

Problem

$X$ is a discrete random variable with range $\{ 1,2,3 \}$ and pmf $f\left( 1 \right)=0.5, f\left( 2 \right)=0.3$ and $f\left( 3 \right)=0.2$ .

• Find $E(X)$
• Find $E\left( X=2 \right)$
• Find $E\left( X=2 \right)$
• Find $E\left( X \right)$
• Find $E\left( X \right)$
• Simplify $E\left( X \right)$
• Simplify $E\left( E\left( X \right) \right)$