12. A rat is required to run a maze and there are 3 exits, Exit 1, Exit 2, and Exit 3. Let Y, denote the number of times Exit I is chosen in successive running. For the following, assume that the rat chooses an exit at random on each run. Find the probability that n = 6 runs result in Y, = 3,Y, =1,Y, = 2 For general n, find E(Y,) and V (Y,) Find Cov(Y,,Y,) for general n (a) (b) (c) (d) To check for the rat's preference between exit 2 and 3, we may look at Y, - Y,. Find E(Y, - Y,) and V (Y, -Y,) for general n.

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12.
A rat is required to run a maze and there are 3 exits, Exit 1, Exit 2, and Exit 3. Let Y, denote
the number of times Exit I is chosen in successive running. For the following, assume that the rat
chooses an exit at random on each run.
(а)
Find the probability that n = 6 runs result in Y, = 3, Y, =1, Y, = 2
(b)
For general n, find E(Y)and V (Y,)
(c)
Find Cov(Y,, Y,) for general n
29
(d)
To check for the rat’s preference between exit 2 and 3, we may look at Y, – Y, .
Find E(Y, – Y,) and V (Y, – Y,) for general n.
2
Transcribed Image Text:12. A rat is required to run a maze and there are 3 exits, Exit 1, Exit 2, and Exit 3. Let Y, denote the number of times Exit I is chosen in successive running. For the following, assume that the rat chooses an exit at random on each run. (а) Find the probability that n = 6 runs result in Y, = 3, Y, =1, Y, = 2 (b) For general n, find E(Y)and V (Y,) (c) Find Cov(Y,, Y,) for general n 29 (d) To check for the rat’s preference between exit 2 and 3, we may look at Y, – Y, . Find E(Y, – Y,) and V (Y, – Y,) for general n. 2
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