A manufacturing unit produces metal tubes with a nominal diameter of 12 in. The actual diameter of a tube can be regarded as a random variable having density function (in inches)

Assuming that the length of each tube is 20 ft, answer the following:
(i) Find the density function and the distribution function of the surface area for a randomly selected tube. (The formula for the surface area is 2πr(r + h), where r is the radius and h is the length [or height] of a tube.)
(ii) If the cost of producing the tubes is k dollars per square inch, calculate the expected cost for each tube produced.

Transcribed Image Text:

f(x)= 0, [1-(12-x)2], 11.5x12.5, elsewhere.