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Real Valued Function

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The lemma is in the attachment along with further questions. The lemma defines a way to rewrite f(X)-f(Xo)

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This solution offers a tentative guide to prove a certain lemma for a valued function. Attached as a .doc file.

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dX0f is the differential of f at Xo and is given by:

(dX0 f)(X) = fx1 (X0)x1 + fx2 (X0)x2 + ...+ fxn (X0)xn

E(X) is the expected value or expectation in probability theory.
Suppose random variable X can take value x1 with probability p1, value x2 with probability p2, and so on, up to value xk with probability ...

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Tania Dey, PhD
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