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# The article "Second Moment Reliability Evaluation vs. ISBN: 9780321629111 32

## Solution for problem 7E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 7E

The article ?"Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" (Quality and Reliability Engr. Intl., 2012: 887496) ?considered the use of a uniform distribution with A = .20 and B = 4.2.5 for the diameter X of a certain type of weld (mm). a. Determine the pdf of X and graph it. b. What is the probability that diameter exceeds 3 mm? c. What is the probability that diameter is within I mm of the mean diameter? d. For any value a satisfying .20 < a < a + 1 < 4.25, what is P(a < X < a + 1)?

Step-by-Step Solution:

Answer : Step 1 of 4 : Given, The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" considered the use of a uniform distribution with A = .20 and B = 4.2.5 for the diameter X of a certain type of weld (mm). a) The claim is to find the probability density function of x. Let X be uniform random variable with intervals (0.20, 4.25), X~U(0.20, 4.25) 1 Probability density function of X is f(x; A, B) = B A where , A = 0.20 and B = 4.25 1 Therefore, f(x; 0.20, 4.25) = 4.25 0.20 1 = 4.05 = 0.2469 Step 2 of 4 : b) The claim is to find the probability that diameter exceeds 3 mm. P(x 3) = 1 - P(0.2 x 3) P(a x b) = (b - a) ×f(x) 1 Where, a = 0.2, b = 3 and f(x) = 4.05 1 P(0.20 x 3) = (3 - 0.20) × 4.05 = 2.8 × 1 4.05 = 56/81 Therefore, P(x 3) = 1 - 56/81 = 25/81 0.3086 be the probability that diameter exceeds 3 mm

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321629111

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