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Statistics / Probability and Statistical Inference 9 / Chapter 7.5 / Problem 7.5-1

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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Let Y1 < Y2 < Y3 < Y4 < Y5 < Y6 be the order statistics of a random sample of size n = 6

Chapter 7, Problem 7.5-1

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QUESTION:

Let Y1 < Y2 < Y3 < Y4 < Y5 < Y6 be the order statistics of a random sample of size n = 6 from a distribution of the continuous type having (100p)th percentile p. Compute (a) P(Y2 < 0.5 < Y5). (b) P(Y1 < 0.25 < Y4). (c) P(Y4 < 0.9 < Y6).

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QUESTION:

Let Y1 < Y2 < Y3 < Y4 < Y5 < Y6 be the order statistics of a random sample of size n = 6 from a distribution of the continuous type having (100p)th percentile p. Compute (a) P(Y2 < 0.5 < Y5). (b) P(Y1 < 0.25 < Y4). (c) P(Y4 < 0.9 < Y6).

ANSWER:

Step 1 of 3

Compute the probability that the random interval includes. That is, let us determine. We have success on a single trial if that X is less than . Thus, the probability of success on each of the independent trials is . The probability that we have at least 2 successes but fewer than 5 successes using the table of the Binominal distribution is

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