Question: Let X be a random variable on (0, 1) whose density is f(x). Show that we can estimate f 1 0 g(x)dx by simulating X

Let X be a random variable on (0, 1) whose density is f(x). Show that we can estimate f¹₀g(x)dx by simulating X and then taking g(X)/f (X) as our estimate. This method, called importance sampling, tries to choose f similar in shape to g, so that g(X)/f(X) has a small variance.

Step by Step Solution

★★★★★

3.46 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The integral of a function fx with respect to x over a given interval can be estimated by simulating ... 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 A First Course In Probability Questions!

Let X be a random variable on a sample space S. Show that V (aX + b) = a2V (X) whenever a and b are real numbers.

Let X be a random variable for which the p.d.f f is as given in Exercise 3. Construct a random variable Y = r(X) for which the p.d.f. g is as given in Exercise 9. 1 -x 0 otherwise. for 0

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in Mesa Verde National Park. Then x has a distribution that is approximately...

15. (a) Verify that the minimum of (4.1) occurs when a is as given by (4.2). (b) Verify that the minimum of (4.1) is given by (4.3). 16. Let X be a random variable on (0, 1) whose density is f(x)....

*30. Let ^ be a random variable on [0, 1] whose density is f(x). Show that we can estimate g(x) dx by simulating X and then taking as our estimate g(X)/f(X). This method, called importance sampling,...

Exercise 3 (18 points) The following statistics have recently been reported by the British Columbia government over a week in December 2021 regarding the number of Covid-19 cases in the province,...

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

You work for a local fitness center called Super Fit. The owners of Super Fit would like to expand their business and add a running track and a large pool. They have drafted the following letter to...

Two concrete spans of a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P19.61a). If a temperature increase of T occurs, what is the height y to which the...

What is the gross profit on these general accounting question? Pineville Furniture Co. manufactured 60,000 units of a product at a total cost of $540,000. The company sold 50,000 units at a price of...

To know that victimless crimes against public decency (the ancient crimes against public morals) generate heated disagreement and debate between those who believe that criminal law should enforce...

Let X(i), i = 1, . . . , n, denote the order statistics from a set of n uniform (0, 1) random variables, and note that the density function of X(i) is given by f(x) = n!/(i 1)!(n i)! xi1(1 x)ni 0...

Show that Y = a + bX, then +1 ifb >0

Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated; give a counterexample to show that the converse is not true. Prove and use the fact that E[XY] = E[XE[Y|X]].

Question 1 Shinoda Corp, has 9.34 percent coupon bonds making annual payments with a YTM of 6.71 percent. The current yield on these bonds is 7.63 percent. How many years do these bonds have left...

Best Co. has 100 million common shares outstanding currently selling for $40/share. It has a dividend yield of 3% (hint: dividend yield is calculated as dividends paid in the last 12 months divided...

Here is some price information on Fincorp stock. Suppose first that Fincorp trades in a dealer market. Bid Asked 55.25 55.50 Suppose you have submitted an order to your broker to buy at market. At...