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An actuary models the lifetime of a device using the random variable Y = 10X0.8, where X is an exponential random variable with mean 1 year. Determine the probability density function f (y), for y > 0, of the random variable Y.

  1. 10y0.8e-8y-0.2
  2. 8y-0.2e-10y0.8
  3. 8y-0.2e-10y0.8
  4. 8y-0.2e-(0.1y)1.25
  5. (0.1y)1.25e-0.125(0.1y)0.25
  6. 0.125(0.1y)0.25e-(0.1y)1.25

Solution: F

 


Therefore,