Question: 3. The random variable X has density function proportional to g(x), where g is a function satisfying g(x) = ( |x|n if |x| 1,

3. The random variable X has density function proportional to g(x), where g is a function satisfying g(x) =

(

|x|−n if |x| ≥ 1, 0 otherwise, and n (≥ 2) is an integer. Find and sketch the density function of X, and determine the values of n for which both the mean and variance of X exist.

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