A learning experiment requires a rat to run a maze (a network of pathways) until it

Chapter 5, Problem 5.119

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A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Yi denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run. a Find the probability that n = 6 runs result in Y1 = 3, Y2 = 1, and Y3 = 2. b For general n, find E(Y1) and V(Y1). c Find Cov(Y2, Y3) for general n. d To check for the rats preference between exits 2 and 3, we may look at Y2 Y3. Find E(Y2 Y3) and V(Y2 Y3) for general n.

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