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The probability density function for the diameter of a drilled hole in millimetres is 10e-(x-5) for x > 5 mm. Although the target diameter

The probability density function for the diameter of a drilled hole in millimetres is 10e-(x-5) for x > 5 mm. Although the target diameter is 5 millimetres, vibrations, tool wear, and other nuisances produce diameters greater than 5 millimetres. (a) Determine the mean and variance of the diameter of the holes. (b) Determine the probability that a diameter exceeds 5.1 millimetres.

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