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It costs 3 to fix each defect what is the expected cost and

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)?

(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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