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If you throw a head I give you $1. If you throw a tail you give me $1. If [tex] R_i [/tex] is the random amount ($1 or -$1) you make on the [tex] ith [/tex] toss then why is: [tex] E[R_i] = 0, E[R^2_i]=1, E[R_iR_j] = 0 [/tex]? If [tex] S_i = \sum^i_{j=1} R_j [/tex] which represents the total amount of money you have won up to and including the ith toss, then why does [tex] E[S_i] = 0, E[S_i^2] = E[R_1^2 + 2R_1R_2 + ...] = i [/tex]? I know that if there had been five tosses already then [tex] E[S_6|R_1,...,R_5] = S_5 [/tex]

Any help is appreciated

Thanks

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# Homework Help: Stochastic Calculus

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