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If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁x₁ + a₂x₂. 0 USE SALT X₁ ↓ a₁ X₂ ↓ a₂ (a) Suppose that X₁ and X₂ are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If a₁ = 9 ft and a₂ = 18 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment kip-ft kip-ft standard deviation (b) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A2, assume that these variables have means of 9 and 18 ft, respectively, that each has a standard deviation of 0.5, and that all A's and X's are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft² (e) If the situation is as described in part (a) except that Corr(X₁, X₂) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft²

If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁x₁ + a₂x₂. 0 USE SALT X₁ ↓ a₁ X₂ ↓ a₂ (a) Suppose that X₁ and X₂ are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If a₁ = 9 ft and a₂ = 18 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment kip-ft kip-ft standard deviation (b) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A2, assume that these variables have means of 9 and 18 ft, respectively, that each has a standard deviation of 0.5, and that all A's and X's are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft² (e) If the situation is as described in part (a) except that Corr(X₁, X₂) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft²

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter16: Table Of Decimal Equivalents And Combined Operations Of Decimal Fractions
Section: Chapter Questions
Problem 34A: A stamped sheet steel plate is shown in Figure 164. Compute dimensions AF to 3 decimal places. All...
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If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁x₁ + a₂x₂. USE SALT X₁ a₁ X₂ a₂ (a) Suppose that X₁ and X₂ are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If a₁ = 9 ft and a₂ = 18 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment kip-ft kip-ft standard deviation (b) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A₂, assume that these variables have means of 9 and 18 ft, respectively, that each has a standard deviation of 0.5, and that all A's and X;'s are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft² (e) If the situation is as described in part (a) except that Corr(X₁, X₂) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft² You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁x₁ + a₂x₂. USE SALT X₁ a₁ X₂ a₂ (a) Suppose that X₁ and X₂ are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If a₁ = 9 ft and a₂ = 18 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment kip-ft kip-ft standard deviation (b) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A₂, assume that these variables have means of 9 and 18 ft, respectively, that each has a standard deviation of 0.5, and that all A's and X;'s are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft² (e) If the situation is as described in part (a) except that Corr(X₁, X₂) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft² You may need to use the appropriate table in the Appendix of Tables to answer this question.
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