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Suppose that contamination particle size (in micrometers) can be modeled as f(x) = 2x-3 for 1 > x and f(x) = 0for x <= 1.
a) Confirm that f(x) is a probability density function.
b) Give that cumulative distribution function.
c) Determine the mean.
d) What is the probability that the size of a random particle will be less than 5 micrometers?
e) An optical device is being marketed to detect contamination particles. It is capable of detecting particles exceeding 7micrometers in size. What proportion of the particles will be detected?
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