Question: Example 16. (Self Practice) Let ( Y ) be the number of firing pins tested until a defective is found in a sample of 5

Example 16. (Self Practice) Let $ Y $ be the number of firing pins tested until a defective is found in a sample of 5 which contains 3 defectives. The probability mass function for $ Y $ is given below.

Suppose that the cost of inspecting of a single pin is $ \$ 300 $ if the pin is defective and $ \$ 100 $ if it is good. Note that the total cost $ C $ (in dollars) of the inspection is given by the equation $ C=200+100 \mathrm{Y} $. Calculate the average and variance of the inspection cost $ C $. ( $ \$ 350 $, 4,500 in $ \$^{2} $ )

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