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Question: 1. Suppose that X and Yare continuous random variables with the joint probability density function
(a) Find k, E(X), E(Y), V(X), V(Y), and cov(X, Y). Are X and Y independent?
(b) Find the marginal densities of X and y.
(c) Find the conditional density of X given Y = ½ and hence E(X|Y = ½) and V( Y|X = ½).
2. Given that y = ex is normal with mean 2 and variance 4, find the mean and variance of x.
1. Use the field axioms and their consequences to prove the following properties of real numbers. Your proofs should be careful and complete, with only one axiom, theorem, or other justification per step.
Stochastic dominance implies that if the same return can be obtained with two different investments, X and Y, yet the likelihood of a return exceeding.
A survey showed that the average commuter spends about 26 minutes on a one-way door-to-door trip from home to work. In addition.
Consider the unconstrained NLP max x1x2 - 5(x1 - 3)4 - 4(x2 - 5)3. Start at the point x(0) = (3,7) and compute 3 iterations of the gradient search to find points x(1), x(2), and x(3). Then make a plot of the 4 solutions (x(0) through x(3)) and show h..
An auto dealership is running a promotional deal whereby they will replace your tires free of charge for the life of the vehicle when you purchase your car.
A company that manufactures automobile parts is weighing the possibility of investing in an FMC (Flexible Manufacturing Cell).
For each case, plot the trajectories of two weights and its corresponding cost with the number of iterations. These two weights should converge to the optimal values as you will give in (a)
Find the range of values of the parameter a for which the function f(x1, x2, x3) = 2x1x3 - x12 - x22 - 5x32 - 2ax1x2 - 4x2x3 is concave
There are three investment plans for your consideration. Each plan calls for an investment of $25,000 and the return will be one year later.
Miller Manufacturing has a target debt-equity ratio of .55. Its cost of equity is 14 percent, and its cost of debt is 5 percent. If the tax rate is 38 percent, what is the company's WACC? (Do not round intermediate calculations and enter your answ..
Your company has purchased a large new truck tractor for over-the-road use (asset class 00.26). It has a cost basis of $180,000.
An industrial coal-fired boiler for process steam is equipped with a 10-year-old electrostatic precipitator (ESP). Changes in coal quality have caused stack.
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