- #1
courtrigrad
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Let's say we restrict 6 coin tosses to a period t so that each toss will take [tex] \frac{t}{6} [/tex]. The size of the bet is [tex] \sqrt{\frac{t}{6}} [/tex]
Then why does [tex] \sum^n_{j=1} (S_{j}-S_{j-1})^{2} = 6 \times(\sqrt{\frac{t}{6}}) = t [/tex]. Or more generally why does:
[tex] \sum^n_{j=1}(S_{j}-S_{j-1})^{2} = n\tiimes(\sqrt{\frac{t}{n}})^{2} = t [/tex]
Also why does [tex] E[S(t)] = 0 , E[S(t)^{2}] = t [/tex]?
Thanks
Then why does [tex] \sum^n_{j=1} (S_{j}-S_{j-1})^{2} = 6 \times(\sqrt{\frac{t}{6}}) = t [/tex]. Or more generally why does:
[tex] \sum^n_{j=1}(S_{j}-S_{j-1})^{2} = n\tiimes(\sqrt{\frac{t}{n}})^{2} = t [/tex]
Also why does [tex] E[S(t)] = 0 , E[S(t)^{2}] = t [/tex]?
Thanks
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