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Suppose that a certain system contains three components that function independently of each other and are connected in series, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component X1 - exp(A = .02), measured in hours; the length of life of the second component X2 exp(A = .07), measured in hours; and the length of life of the third component X3 v exp(A = .11), measured in hours. (a) Suppose that the random variables X1, X2, X3 are independent and Xi - exp(Ai) for i = 1, 2, 3. Let Y1 = min(X1, X2, X3). Determine the distribution for Y1. (b) Determine the probability that the system will not fail before 8 hours.

Suppose that a certain system contains three components that function independently of each other and are connected in series, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component X1 - exp(A = .02), measured in hours; the length of life of the second component X2 exp(A = .07), measured in hours; and the length of life of the third component X3 v exp(A = .11), measured in hours. (a) Suppose that the random variables X1, X2, X3 are independent and Xi - exp(Ai) for i = 1, 2, 3. Let Y1 = min(X1, X2, X3). Determine the distribution for Y1. (b) Determine the probability that the system will not fail before 8 hours.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Suppose that a certain system contains three components that function independently of each other and are connected in series, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component X1 - exp(A = .02), measured in hours; the length of life of the second component X2 v exp(A = .07), measured in hours; and the length of life of the third component X3 v exp(A = .11), measured in hours. (a) Suppose that the random variables X1, X2, X3 are independent and Xi v exp(Ai) for i = 1, 2, 3. Let Y1 = min(X1, X2, X3). Determine the distribution for Y1. (b) Determine the probability that the system will not fail before 8 hours.
Transcribed Image Text:Suppose that a certain system contains three components that function independently of each other and are connected in series, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component X1 - exp(A = .02), measured in hours; the length of life of the second component X2 v exp(A = .07), measured in hours; and the length of life of the third component X3 v exp(A = .11), measured in hours. (a) Suppose that the random variables X1, X2, X3 are independent and Xi v exp(Ai) for i = 1, 2, 3. Let Y1 = min(X1, X2, X3). Determine the distribution for Y1. (b) Determine the probability that the system will not fail before 8 hours.
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