Two different limit states are created from the same two random variables G1-R-S, G2-In(R/S); R N(10,2), S-N(6,), R & S are S.I PartShow by Monte Carlo simulation that the probability of failure for both G1 and G2 is pf-0.0366. In this case we already know the exact solution, so we can determine the number of simulations N needed to gain a desired precision in our estimated (sample) probability of failure. We will define precision as the coefficient of variationof the sample probability of failure. This is defined in tems of the exact probability of failure and N as: V Use this to determine the N.pf N necessary to get V-0.05, and use this value for your simulations to show pf-0.0366 Show that the precision for your sample pf is V = 0.05 for both G1 and G2. To do this you need many samples of pf, from which you measure-std(pf mean pf). Estimate pfGI and pfG2 2000 times, each time using the N you calculated for 0.05. Use these 2000 estimates of pfGl and pfG2 to calculate the Vassociated with each and report. Part II: Back to a single estimate for both pfG1 and pfG2. Create a histogram of G1 and G2 from your simulations and plot the normalized versions together on the same graph. To do this, use the MATLAB command 'hist' using 100 bins. For G, for example: [pdfGI,xG1 histG,100) pdfGI-pdfGl/trapz(xGl,pdfG) plot(xGl.pdfG1); hold on Same for G2 Measure from your simulations the skewness and kurtosis for both Gl and G2 and place these values on the plot you created above. Investigate the Matlab commands 'text' and 'gtext' to learn how to place numbers or text on an existing plot. Part III: Show numerically that the reliability index for the two limit states are G1.79-1.84 Provide the estimated prob( fail) for each reliability index using (-B). Use the Matlab command normcdf. Using the information you have produced, comment on the accuracy of using the reliability index to estimate probability of failure for each of the two limit states. Two different limit states are created from the same two random variables G1-R-S, G2-In(R/S); R N(10,2), S-N(6,), R & S are S.I PartShow by Monte Carlo simulation that the probability of failure for both G1 and G2 is pf-0.0366. In this case we already know the exact solution, so we can determine the number of simulations N needed to gain a desired precision in our estimated (sample) probability of failure. We will define precision as the coefficient of variationof the sample probability of failure. This is defined in tems of the exact probability of failure and N as: V Use this to determine the N.pf N necessary to get V-0.05, and use this value for your simulations to show pf-0.0366 Show that the precision for your sample pf is V = 0.05 for both G1 and G2. To do this you need many samples of pf, from which you measure-std(pf mean pf). Estimate pfGI and pfG2 2000 times, each time using the N you calculated for 0.05. Use these 2000 estimates of pfGl and pfG2 to calculate the Vassociated with each and report. Part II: Back to a single estimate for both pfG1 and pfG2. Create a histogram of G1 and G2 from your simulations and plot the normalized versions together on the same graph. To do this, use the MATLAB command 'hist' using 100 bins. For G, for example: [pdfGI,xG1 histG,100) pdfGI-pdfGl/trapz(xGl,pdfG) plot(xGl.pdfG1); hold on Same for G2 Measure from your simulations the skewness and kurtosis for both Gl and G2 and place these values on the plot you created above. Investigate the Matlab commands 'text' and 'gtext' to learn how to place numbers or text on an existing plot. Part III: Show numerically that the reliability index for the two limit states are G1.79-1.84 Provide the estimated prob( fail) for each reliability index using (-B). Use the Matlab command normcdf. Using the information you have produced, comment on the accuracy of using the reliability index to estimate probability of failure for each of the two limit states