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A power-electronics cooling fan is assumed to have an exponentially distributed operating lifetime , measured in hours, with PDF The manufacturer's stated mean operating lifetime is 2000 h.
(a) Determine the rate parameter , including its units.
(b) Determine the variance and standard deviation of .
(c) An engineer claims that because the mean lifetime is 2000 h, most fans should fail close to 2000 h. Briefly explain why the exponential model does not support this interpretation.
Show all relevant working. (Note: You do
Hand your answer sheet to the teaching team at the end of the mid-semester test.
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