2.5.1 Use the law of total probability for conditional expectations E[EfXjY;ZgjZ] D E[XjZ] to show E[XnC2jX0; :

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2.5.1 Use the law of total probability for conditional expectations E[EfXjY;ZgjZ] D E[XjZ] to show E[XnC2jX0; : : : ;Xn] D E[EfXnC2jX0; : : : ;XnC1gjX0; : : : ;Xn]:

Conclude that when Xn is a martingale, E[XnC2jX0; : : : ;Xn] D Xn:

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