Suppose that in the situation of the two-armed bandit problem in Section 2.7, you follow the strategy suggested there.

(a) Show that (i) if you lose at the first time, then you will switch; (ii) if you win at the first time, and p₁ < 1/2 , then you will never switch at the second time.

(b) Let p₁ = 0.3, p₂ = 0.2. Suppose you won at the first time, and after that began to lose in each play. At which moment will you switch?

(c) For the previous problem, arrange a file in Excel, or write a program using another software, allowing you to find the moment of switch for any p₁, p₂.