After manufacture, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents values of the cumulative distribution function F(x)of X.
a. What is the probability that two or fewer errors are detected?
b. What is the probability that more than three errors are detected?
c. What is the probability that exactly one error is detected?
d. What is the probability that no errors are detected?
e. What is the most probable number of errors to be detected?
(a) P(X ? 2) = F(2) = 0.83
(b) P(X >3) = 1 ? P(X ? 3) = 1 ? F(3) = 1 ? 0.95 = 0.05
(c) P(X = 1) = P(X ? 1) ? P(X ? 0) = F(1) ? F(0) = 0.72 ? 0.41 = 0.31
(d) P(X = 0) = P(X ? 0) = F(0) = 0.41
(e) For any integer x, P(X = x) = F(x) ? F(x ? 1) [note that F(?1) = 0]. The value of x for which this quantity is greatest is x = 0.
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