Question: With reference to Definition 4.4, show that 0 = 1 and that 1 = 0 for any random variable for which E(X) exists.

With reference to Definition 4.4, show that µ0 = 1 and that µ1 = 0 for any random variable for which E(X) exists.

Definition 4.4

The rth moment about the mean of a random variable X, denoted by µr, is the expected value of ( X – µ)r, symbolically

4, = E[(X-uY] = Ea-u f)

For r = 0, 1, 2, . . . , when X is discrete, and

When X is continuous.

4, = E[(X-uY] = Ea-u f)

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