CE 7070 HW#2: RV Functions and Moments excel w/ graphs 1. Forty-Five 2x10 timber beams were tested for modulus of rupture (MOR). The results are shown below (psi): 4464 5001 4880 6486 5897 3758 5974 5023 5085 4764 3508 4705 6044 3600 7145 5072 5693 3845 5288 4830 5130 3966 5702 4310 5133 5802 7022 4590 5289 5866 4627 4930 5772 4724 6408 4667 5332 3973 5331 4209 4434 3982 3521 5184 5437 a) Graph the PMF and the CDF. b) Plot the frequency and cumulative frequency histograms. c) Calculate the first four moments and their nondimensionalized coefficients. calculate w/ hands 2. Assume the moment capacities of a number of reinforced-concrete beams tested in the laboratory are normally distributed with mean = 100 k-ft and standard deviation = 15. a) What proportion of the beams are expected to have moment capacities that fall within 100 and 135? b) What proportion are expected to exceed 140? 3. For a particular class, a student takes two exams. For the first exam, the student scored 80 and the class average was 70 with variance 100. For the second exam, the student scored 85 and the class average was 75 with variance 225. Relative to the class, on which exam did the student perform better? 4. A given PDF has a bi-linear shape such that it is uniform (i.e. horizontal line) between x=0 to x=15 and thereafter decreases linearly zero at x=25. Determine: a) the equation for the CDF b) PCR 0. Find: a) an equation for the CDF b) the first three moments and their nondimensionalized coefficients Note: you may use any computational tool available to conduct the integrations. CE 7070 HW#2: RV Functions and Moments excel w/ graphs 1. Forty-Five 2x10 timber beams were tested for modulus of rupture (MOR). The results are shown below (psi): 4464 5001 4880 6486 5897 3758 5974 5023 5085 4764 3508 4705 6044 3600 7145 5072 5693 3845 5288 4830 5130 3966 5702 4310 5133 5802 7022 4590 5289 5866 4627 4930 5772 4724 6408 4667 5332 3973 5331 4209 4434 3982 3521 5184 5437 a) Graph the PMF and the CDF. b) Plot the frequency and cumulative frequency histograms. c) Calculate the first four moments and their nondimensionalized coefficients. calculate w/ hands 2. Assume the moment capacities of a number of reinforced-concrete beams tested in the laboratory are normally distributed with mean = 100 k-ft and standard deviation = 15. a) What proportion of the beams are expected to have moment capacities that fall within 100 and 135? b) What proportion are expected to exceed 140? 3. For a particular class, a student takes two exams. For the first exam, the student scored 80 and the class average was 70 with variance 100. For the second exam, the student scored 85 and the class average was 75 with variance 225. Relative to the class, on which exam did the student perform better? 4. A given PDF has a bi-linear shape such that it is uniform (i.e. horizontal line) between x=0 to x=15 and thereafter decreases linearly zero at x=25. Determine: a) the equation for the CDF b) PCR 0. Find: a) an equation for the CDF b) the first three moments and their nondimensionalized coefficients Note: you may use any computational tool available to conduct the integrations