MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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18. Busy Phone Lines. An administrative office has eight incoming telephone lines. The probability distribution of the number of busy lines, Y, is as follows. • 0 1 2 3 4 5 6 7 8 y P(Y = y) 0.033 0.124 0.202 0.214 0.1287 0.105 0.099 0.0543 0.04 Use random-variable notation to express each of the following events. The number of busy lines is a. exactly five. c. between two and six, inclusive. d. at least one. Apply the special addition rule and the probability distribution to de- termine b. at least five. f. P(Y < 5). h. P(Y > 1). e. P(Y = 5). g. P(1 < Y < 6). 19. Busy Phone Lines. Refer to the probability distribution dis- played in the table in Problem 18. a. Find the mean of the random variable Y. b. On average, how many lines are busy? c. Compute the standard deviation of Y. d. Construct a probability histogram for Y; locate the mean; and show one-, two-, and three-standard-deviation intervals.
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Transcribed Image Text:18. Busy Phone Lines. An administrative office has eight incoming telephone lines. The probability distribution of the number of busy lines, Y, is as follows. • 0 1 2 3 4 5 6 7 8 y P(Y = y) 0.033 0.124 0.202 0.214 0.1287 0.105 0.099 0.0543 0.04 Use random-variable notation to express each of the following events. The number of busy lines is a. exactly five. c. between two and six, inclusive. d. at least one. Apply the special addition rule and the probability distribution to de- termine b. at least five. f. P(Y < 5). h. P(Y > 1). e. P(Y = 5). g. P(1 < Y < 6). 19. Busy Phone Lines. Refer to the probability distribution dis- played in the table in Problem 18. a. Find the mean of the random variable Y. b. On average, how many lines are busy? c. Compute the standard deviation of Y. d. Construct a probability histogram for Y; locate the mean; and show one-, two-, and three-standard-deviation intervals.
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