Question

The density function of the thickness of a conducive coating in micrometers is f(x) =

600x^−2

for 100 < x < 120.

a) Determine the mean and variance of the coating thickness.

b) If the coating costs $0.50 per micrometer of thickness on each part, what is the

average cost of the coating per part?

Answer 1

$a:\\EX=\int_{100}^{120}{x\cdot \frac{600}{x^2}dx}=600\ln x|_{100}^{120}=600\ln 1.2\\EX^2=\int_{100}^{120}{x^2\cdot \frac{600}{x^2}dx}=12000\\DX=EX^2-\left( EX \right) ^2=12000-\left( 600\ln 1.2 \right) ^2=33.186\\b:\\S=0.5EX=300\ln 1.2$