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The distribution of life length X (years) of a defective component in a batch of your...

  1. The distribution of life length X (years) of a defective component in a batch of your “generic” water quality meter is given by the pdf     f(x)       = 0       if x < 0 = e-x      if x ≥ 0

  2. For the defective water quality meter example above suppose you bought one of these meters and you are not certain whether it came from the batch with the defective component. How long (to the nearest year) should this instrument work without failing for you to conclude that it did not come from the batch with the defective component?

[Hint: Approach this as a test of a null hypothesis with a = 0.05]

  1. Write the formula of the cdf, F(x).
  2. Sketch the cdf.
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