Consider the random variable: Where each Bi is obtained as a result of the toss of a
Question:
Consider the random variable:
Where each Bi is obtained as a result of the toss of a fair coin:
We let n = 4 and consider X4.
(a) Calculate the E [X4| I1], E [X4| I2], E [X4| I4]
(b) Let
Zi = E [X4| Ii]
Is Zi, I = 1. . . 4, a martingale?
(c) Now define:
Vi = Bi + ?i
And
Is Vi a martingale?(d) Can you convert Vi into a martingale by an appropriate transformation?(e) Can you convert Vi into a martingale by changing the probabilities associated with a cointoss?
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a EX 4 I 1 X 1 EX 4 I 2 X 2 and EX 4 I 4 X 4 b If Z i EX 4 ...View the full answer
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