Midterm Review 

Alice and Bob are going to study for the upcoming midterm together. They agree to meet at time t this afternoon. Alice will show up X hours after t, where X ∈ Uniform[0,2]. Bob’s arrival time is more unpredictable. He will be distracted by Pokemon Go and will show up Y hours after t, where Y ∈ Expo(1). The person who shows up later is late for T hours. What is E[T]? (Hint: some useful integrals ???? x2e−xdx = −e−x(x2 +2x+2)+c and ???? −xe−xdx = xe−x +e−x +c)