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Question: 1. Use partial derivatives of F(α, β) to show that E(X2Y2) = 2σ12σ22ρ2.
2. Show that E(X2Y2) = E(X2)E(Y2)+2E(XY)2.
3. Use integration by parts or the Beta function to show that
From the exercise we can conclude that c = N + 1; therefore we have the pdf P(x|D). Now we want to estimate x itself. One way to do this is to calculate the expected value of this pdf, which, according to the exercise, is (n + 1)/(N + 2). So even though we do not know x, we can reasonably say (n + 1)/(N + 2) is the probability that the next ball will end up in region A, given the behavior of the previous N balls. There is a second way to estimate x; we can find the value of x for which the pdf reaches its maximum. A quick calculation shows this value to be n/N. This estimate of x is not the same as the one we calculated using the expected value but they are close for large N. What is controversial here is the decision to treat the positioning of the line as a random act, whereby x becomes a random variable, as well as the selection of a specific pdf to govern the random variable x. Even if x were a random variable, we do not necessarily know its pdf. Bayes takes the pdf to be uniform over [0, 1], more as an expression of ignorance than of knowledge. It is this broader use of prior probabilities that is generally known as Bayesian methods and not the use of Bayes' Rule itself.
Which of the following is not a source of technological advancement for a producer? better trained workers, more efficient physical capital, higher skill level of managers or outsourcing some aspect of production
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Find the extiction probability for this branching process - give a condition for sure extinction.
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specify the sequence of transformations that will yield the graph of the given function from the graph of f(x) =x^3
Selected identify a qualitative and quantitative variable. Explain what the data set is and why each of the variables you selected are qualitative or quantitative and identify the level of measurement for those variables and if they are continuous..
Suppose that the market equilibrium price for a basic medical check-up is $50, in a market in which there is no health insurance.
A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:
Apply Runge Kutta method to find approximate of y for x = 0.2, in steps of 0.1, if dy/dx = x+y2, given that when x=0.
A rectangular enclousure must have an area of at least 700 yards. If 160 yd of fencing is to be used, and the width cannot exceed the length, what limits must the width of the enclosure lie?
Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) converges uniformly. What is its limit?
If t=0 at the start, for what values of t will the velocity of the particle A exceed the velocity of particle B.
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