The thickness (X) of a wooden shim (in (mathrm{mm}) ) has probability density function a. Find (mu_{X}).
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The thickness \(X\) of a wooden shim (in \(\mathrm{mm}\) ) has probability density function
a. Find \(\mu_{X}\).
b. Find \(\sigma_{X}^{2}\).
c. Let \(Y\) denote the thickness of a shim in inches ( \(1 \mathrm{~mm}=0.0394\) inches). Find \(\mu_{Y}\) and \(\sigma_{Y}^{2}\).
d. If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.
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