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A random variable X has probability density function f(x) defined by f(x) = cx−6 if x...

A random variable X has probability density function f(x) defined by f(x) = cx−6 if x > 1, and f(x) = 0, otherwise.

a. Find the constant c.
b. Calculate E(X) and Var(X).

c. Now assume Z1, Z2, Z3, Z4 are independent RVs whose distribution is identical to that of X. Compute E[(Z1 +Z2 +Z3 +Z4)/4] and Var[(Z1 +Z2 +Z3 +Z4)/4].

d. Let Y = 1/X, using the formula to find the pdf of Y.

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