The random variable (Y) has the (operatorname{PDF} f(y)=y^{-2} I_{[1, infty)}(y)). (a) Find the mean of (Y). (b)

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The random variable \(Y\) has the \(\operatorname{PDF} f(y)=y^{-2} I_{[1, \infty)}(y)\).

(a) Find the mean of \(Y\).

(b) Can you find the first 100 moments about the origin (i.e., \(\mu_{1}^{\prime}, \mu_{2}^{\prime}, \ldots, \mu_{100}^{\prime}\) ) for the random variable \(Y\), why or why not?

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