Question: Consider approximating an expected value I for a uniform random variable U with a function f, I = E[(U)], U~U(0,1). Assume that the independent

Consider approximating an expected value I for a uniform random variable U with a function f, I = E[F (U)], U~U(0,1). Assume

Consider approximating an expected value I for a uniform random variable U with a function f, I = E[(U)], U~U(0,1). Assume that the independent and identical uniform samples U, U, ..., UM can be generated from a pseudo random number generator, then answer the following questions. (a) Find a standard Monte Carlo estimator IM to estimate I. M (b) Find the Monte Carlo estimator with an antithetic variate to estimate I. When does the antithetic variate estimator guarantee the greater performance than a standard Monte Carlo estimator? Explain the reason. (c) Find the Monte Carlo estimator with a control variate to estimate I. When does the control variate estimator guarantee the greater performance than a standard Monte Carlo estimator? Explain the reason.

Step by Step Solution

★★★★★

3.46 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Standard Monte Carlo estimator Im 1M sumfUi for i 12M b Antithetic variate estimator I 1M sumfUi f... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Find a transformation which will change a uniform random variable into each of the following distributions (see Appendix D for the definitions of these distributions if necessary): (a) arcsine, (b)...

Calculate the coefficient of kurtosis for a uniform random variable defined over the unit interval, fY (y) =1, for 0 y 1.

Compute the variance for a uniform random variable defined on the unit interval.

Suppose you are given the following information. The beta of company, bi, is 0.9, the risk free rate, rRF, is 6.8%, and the expected market premium, rM-rRF, is 6.3%. Because your company is larger...

Consider the problem of generating a random sample Iron, a specified distribution on a single variable. You can assume that a random number generator is available that returns a random number...

Suppose that an estimate of the power spectrum of a signal is obtained by the method of avetraging periodograms, as discussed in Section 10.6.3 This is, the spectrum estimate is? where the K...

For the van der Waals interaction with potential-energy function given by Eq. (13.25), show that when the magnitude of the displacement x from equilibrium (r = Ro) is small, the potential energy can...

Suppose that a function f is continuous on [0, 1] except at 0.25 and that f (0) = 1 and f(1) = 3. Let N = 2. Sketch two possible graphs of f, one showing that f might not satisfy the conclusion of...

A block of mass m is connected to a spring with spring constant k, and oscillates on a horizontal, frictionless surface. The other end of the spring is fixed to a wall. If the amplitude of...

Suppose that the probabilities are 0.4. 0.3, 0.2, and 0.1, respectively, that 0, 1, 2 or 3 power failures will strike a certain subdivision in any given year. Find the mean and variance of the random...

Compare the strengths and weaknesses of different modes of transportation.

Walk & Talk Inc. makes walkie talkies - handheld, portable, two-way radio transceivers. They are used in setting where mobile phone communication may be costly or impractical, including outdoor...

Question 17 Assume that a firm has EBIT of $15,584,650, a tax rate of 40.0 percent, total invested capital of $68,600,000, and a weighted average cost of capital (WACC) of 12.904 percent. Given this...

How do the following situations illustrate the features of psychological egoism and/or ethical egoism, or how do they illustrate the limitations and challenges to psychological egoism and ethical...

differentiate the function ( x + 1 ) / ( x ^ 3 + x - 6 )

For a voltage V-210 sin 170xt, find the root-mean-square voltage for one period. Vrms = (Round to the nearest integer as needed.)

Clonex Labs. Incorporated, uses the weighted-average method in its process costing system. The following data are available for on department for October. The department started 392,000 units into...

Determine the annual percentage yield for a loan that charges a monthly interest rate of 1.5% and compounds the interest monthly.

Suppose X is a Rician random variable with a PDF given by Derive an expression for E [euX2]. Note that this is not quite the moment- generating function, but it can be used in a similar way. f(x) =...

Calculate the spectrum for in Exercise 11.5 if And 0, otherwise.

Suppose we are allowed to observe a random process Z (t) at two points in time, to and t1. Based on those observations we would like to estimate Z (t) at time t= t2 where t0

What is your assessment of the job Michael Dell has done in his roles as the companys CEO and Chairman? What grade would you give him for his leadership of the company over the past 20+ years? Has he...

Assuming cost of goods sold as a percent of sales is constant and that operating costs are fixed, what would the companys 2011 pro forma income statement look like after implementing your...

Based on your responses to the previous questions, identify some strategic options for Respironics. Should it expand geographic markets, invest in and apply new technology, identify and serve a...