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The lifetime X (in years) of a machine has a probability density function (pdf): ?(?) =...

The lifetime X (in years) of a machine has a probability density function (pdf):

?(?) = ??−?⁄?,    ? > 0; ? > 0.

  1. Find the value of the parameter ?. Give the two names of this distribution.
  2. Find E(X), Var(X), and ?(?5?−?⁄3).
  3. Find the constant c such that P(X > c) = 0.95.
Math   Statistics-And-Probability   
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