Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

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Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Suppose X0 = 50. Let T = min{j : Xj = 0 or 100}. Let Fn denote the information contained in X1,··· ,Xn.

(1) Verify that Xn is a martingale.

(2) Find P (XT = 100).

(3) Let Mn = Xn2 − n. Verify that Mn is also a martingale.

(4) It is known that Mn and T satisfy the assumptions of Optimal Sampling The-

oremandhenceE(MT)=E(M0). UsethisfacttofindoutE(T).

math Statistics-And-Probability

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Answer 1

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Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

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Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

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2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are...

3. Suppose X1,X2, are independent identically distributed random variables with mean μ and variance σ2. Let So = 0 and for n > 0 let Sn denote the partial sumi Let Fn denote the information co...

- Let {Xn} denote a sequence of iid random variables such that P(Xi = 1) =...

2. Let Xn, n > 1, be a sequence of independent r.v., and Øn (t) =...

Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

Homework Answers

Add Answer to: Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...

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2. Let Xn,n0,1,2,... denote a biased random walk given by Xo 0 and Xn+1 Xn + YTHI, where (X } are...

3. Suppose X1,X2, are independent identically distributed random variables with mean μ and variance σ2. Let So = 0 and for n > 0 let Sn denote the partial sumi Let Fn denote the information co...

- Let {Xn} denote a sequence of iid random variables such that P(Xi = 1) =...

2. Let Xn, n > 1, be a sequence of independent r.v., and Øn (t) =...

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Let Xn is a simple random walk (p = 1/2) on {0, 1, · · · , 100} with absorbing bound- aries. Supp...