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Stochastic Calculus: Conditional Expectation
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[QUOTE="mjc123, post: 6861687, member: 610180"] No, they are not. The answer for E(S[SUB]n[/SUB][SUP]2[/SUP]) is wrong for n = 2, and that for E(S[SUB]n[/SUB][SUP]3[/SUP]) is wrong for n = 3. The answer you gave in post #4 for E(S[SUB]n[/SUB][SUP]2[/SUP]) is right, but the answer for E(S[SUB]n[/SUB][SUP]3[/SUP]) is not. You didn't show your working, but I suspect the mistake may lie in enumerating the terms of different kinds. There are n terms of the form X[SUB]i[/SUB][SUP]3[/SUP], each of which has expectation -1/3. There are 3n(n-1) terms of the form X[SUB]i[/SUB][SUP]2[/SUP]X[SUB]j[/SUB], each of which has expectation -1/3*1. There are n(n-1)(n-2) terms of the form X[SUB]i[/SUB]X[SUB]j[/SUB]X[SUB]k[/SUB], each of which has expectation -1/27. (Check that the total number of terms is n[SUP]3[/SUP].) [/QUOTE]
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