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The number of defects in a machine-made product is a random variable, X, with the following probability distribution:
x P(X = x)
0 0.2
1 0.1
2 0.2
3 0.3
4 0.2
(a) Find the cumulative distribution function of X.
(b) What is the probability P(1 < X ≤ 3)? P(1 ≤ X ≤ 3)?
(c) Calculate the expected value of X and the standard deviation of X.
(d) It costs $3 to fix each defect. What is the expected cost and the standard deviation of cost of fixing a defect in a product?
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