Bandit Algorithms

2.9 Exercises 44

2.17 Demonstrate using an example that in general, for dependent random
variables,E[XY] =E[X]E[Y] does not hold.

2.18 Prove Proposition 2.8.

Hint Argue thatX(ω) =

∫

[0,∞)I{[0,X(ω)]}(x)dxand exchange the integrals.
Use the Fubini-Tonelli theorem to justify the exchange of integrals.

2.19Prove Theorem 2.12.

2.20Prove Theorem 2.14.