No Assigned Description 1 1/19/2000 In Probabilistic Risk Assessment (PRA), risk profiles are generated for likelihoods as a function of outcomes. Consider the likelihood density function: C exp (-Cx), for the outcome x. Use a plotting routine to plot the following risk profiles:1. The likelihood density function as a function of x. 2. Derive the expression for the cumulative likelihood density function then plot it as afunction ox x. 3. Derive the expression for the complementary cumulative likelihood density function then plot it as a function of x. This is designated as the Farmer's Curve. Use the same scale for comparison, and briefly explain the meaning conveyed by each one of these plots. 2 1/24/2000 In the Rain Hazard Risk Management problem, if the elementary utility U21 is increased to 0.9, implying that carrying the umbrella is a minor burden, how would that affect the decision?Calculte the "break-even" point for the utility U21, at which it makes no difference whether umbrella is carried or not. 3 1/26/2000 Modified Problem 1.4 in textbook.Consider a specific trade-off problem of your choice (e. g.  motor-cycle racing, sky-diving, investing in internet stocks, etc.), where loss (e.g. fatality) is measured by monetary loss. Draw a schematic diagram where outcome probability and cost are represented by horizontal and vertical axes, respectively. Does the concept of "homeostasis" apply in this case? 4 1/31/2000 Consider a risk avert decision making process with the following lottery:1. Loss of  zero dollars with probability  p=0.5. 2. Loss of 1000 dollars with probability p=0.5. Draw a diagram displaying the risk management process for a point A  on the neutral line at an expected loss of 500 DOLLARS. Show a point C having the same loss significance as point A on the loss significance curve. Show a point D with an equivalent significance to a loss of 500 dollars. Compare the decision making process for a risk manager between the operational points A, C and D. 5 2/2/2000 Consider a risk prone decision making process with the following lottery: 1. Loss of  zero dollars with probability  p=0.5. 2. Loss of 1000 dollars with probability p=0.5. Draw a diagram displaying the risk management process for a point A  on the neutral line at an expected loss of 500 DOLLARS. Show a point C having the same loss significance as point A on the loss significance curve. Show a point D with an equivalent significance to a loss of 500 dollars. Compare the decision making process for a risk manager between the operational points A, C and D. Now compare the situation in this problem to the one in the previous problem. In case of non-monetary values, such as human fatalities, in which way would the two risk management approaches differ? 6 2/7/2000 Prove that the Cost Benefit ALARA regulatory Quantitative Design Objective (QDO) of \$1,000 per (person.rem) of averted dose corresponds to 7.4 million dollars per fatality averted.Hint: Use the slope of the Fatality dose graph generated for high radiation doses with linear extrapolation to the low doses. 7 2/9/2000 For the Light Water Reactors (LWRs) Title 10, Code of Federal regulations (CFR) Part 20 , Appendix 1 Lower bound design goals for :1. Liquid effluents activity, 2. Gaseous effluents activitiy, 3. Radioactive Iodine and other activity, use the ratio of 135 fatalities per (1 million person.rems) to calculate the expected fatalities due to these values. Do the values comply with the individual lower risk bound L propposed by Wilson? How do they compare to the de minimis risk? 8 2/14/2000 Generate and plot the Farmer's curve risk profile curve generated by the Cause-Consequence analysis for the problem of an industrial motor overheating and causing a fire.Show on your plot the \$100, \$300, and \$900 constant risk lines, and identify the region of acceptable risk. 9 2/21/2000 Construct a table showing the different failure types classified as to their why, when, where and how causes.Give a one line example of a fault for each one of these types. 10 2/23/2000 Discuss the differences between:1. Fail-safe Designs. 2. Fail-Soft designs. 3. Robust designs. 11 3/27/2000 Use the Computational Fluid Dynamics CFD) code covered in the class to simulate the time and space propagation of a pressure spike(representing a steam explosion) in a gaseous medium obeying the gamma equation of state. 12 3/29/2000 Describe the risk assessment of a financial equivalent to the risk assessment of nuclear, railway. oil tanker, and infectious epidemic accident scenarios. 13 4/12/2000 Redraw the master logic diagrams for the three events:1. Offsite radioactive release 2. Station Blackout 3. AFWS Failure into standard fault tree diagrams using the AND and OR logic gates.