Apollo is uncertain of how he feels about Olga. He thinks she makes him happy, but he is not sure. Below is the joint distribution for whether Olga is around, X ≡1{Olga around}, and whether Apollo is happy, Y ≡1{Apollo is happy}

Joint distribution

X = 0 X = 1
Y = 0 0.4 0.0
Y = 1 0.3 0.3

1. Let A be an arbitrary event. How should we interpret E[1{A}]?

2. Would you say Apollo is a happy person? Why or why not?

3. Would you say Apollo is often around Olga? Why or why not?