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 \(E\left( E\left( X \right) \right)\)