Reliabilty Theory Questions

These questions are a part of a Operations Research class with a section on Reliability Theory. (See attached file for full problem description with proper symbols and equations) --- Question Let N be a non-negative, integer-valued random variable, Show that P{N > 0} >= (E[N])2 E[N ]2 And explain how this inequality can be used to derive additional bounds on a reliability function. HINT: E[N ]2 = E[N 2|N > 0]P{N > 0} (Why?) >= (E[N |N > 0])2P{N > 0} (Why?) Now multiply both sides by P{N > 0}. ---

Reliability Theory Questions

Consider a structure in which the minimal path sets are {1, 2, 3} and {3, 4, 5} a. What are the minimal cut sets? b. If the component lifetimes are independent uniform (0,1) random variables, determine the probability that the system life will be less than ½ .

Using Data Regression to predict sales

(See attached file for full problem description) --- YEAR GNP ln(gnp) 1975 1060 6.966024187 1976 1170 7.064759028 1977 1305 7.17395832 1978 1455 7.28276118 1979 1630 7.396335294 1980 1800 7.495541944 1981 2000 7.60090246 1982 2220 7.705262475 1983 2450 7.803843304 1984 2730 7.912056888 The US BNP during the years 1975-1984 is given in the above table. a. Plot x = years after 1974 against GNP, and use the plot to describe how to fit a curve that could be used to predict GNP during future years. b. When the regression on transformed data is done, we find the B=6.86 and B1=0.105. What is the prediction for 1985 GNP? ---

Additional help with Multiple Regression.

--- Quarter Potential Advertising Season Sales Customers (thousands of dollars) (millions) (thousands) 1 100 30 Winter 1,200 2 105 20 Spring 880 3 111 15 Summer 1,800 4 117 40 Fall 1,050 5 122 10 Winter 1,700 6 128 50 Spring 350 7 135 5 Summer 2,500 8 142 40 Fall 760 9 149 20 Winter 2,300 10 156 10 Spring 1,000 11 164 60 Summer 1,570 12 172 5 Fall 2,430 13 181 35 Winter 1,320 14 190 15 Spring 1,400 15 200 70 Summer 1,890 16 210 25 Fall 3,200 17 221 30 Winter 2,200 18 232 60 Spring 1,440 19 243 80 Summer 4,000 20 264 60 Fall 4,100 a. Use this data and multiple regression to make predictions for the motel chain's sales during the next 4 quarters. As... click for more

I never used LINDO before, need help setting up an example in lindo

I want to know how to use Lindo to solve an example in my textbook. Please need detail instructions so I can feel comfortable using LINDO to solving larger problems, The example in the text uses excel spreadsheet, but I want to know how to use LINDO without excel. How do I write out the objective function, supply and demand constraints and how do I use LINDO, step by step to find minimum cost production plan that meet the demand of each product within the given time limit of each plant? How do I write out the dual out? Describe the economic interpretation for dual problem. Would the mmgt save $ by increasing capacity for city 1 and city 3. Is it benefial to increase the capacity for city... click for more