Question: Suppose (X, Y) are distributed uniformly on the circle of radius 1 centered at the origin. Find the marginal densities of X and Y. Are

Suppose (X, Y) are distributed uniformly on the circle of radius 1 centered at the origin. Find the marginal densities of X and Y. Are X and Y independent?

Step by Step Solution

★★★★★

3.35 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The area of the circle is so fx y 1 where 1 ... 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 Probability With Applications Questions!

A random point (X, Y) is distributed uniformly on the square with vertices (1, 1), (1,-1), (-1,1), and (-1,-1). That is, the joint pdf is /(x, y) = 1/4 on the square. Determine the probabilities of...

The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is (a) Show that 1/c = area of region R. Suppose that (X, Y) is...

Use the acceptreject method to simulate points uniformly distributed on the circle of radius 1 centered at the origin. Use your simulation to approximate the expected distance of a point inside the...

3. (Integral Estimation using Monte Carlo Simulation) (40 points) One application of Monte Carlo Simulation is estimating a difficult to evaluate integral. In this ques- tion, we will perform a...

These practice problems will be very similar to what is on the exam. Make sure you understand how to work these problems, as you will be graded on your process, not the final answer. 3. (Integral...

15. The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is $$f(x, y) = \begin{cases} c &\text{if } (x, y) \in R \\ 0...

Let X 1 , . . . , X n be independent random variables each uniformly distributed on [1, 1]. Let p n = P(X 2 1 + + X 2 n

Let X and Y denote, respectively, the x- and y-coordinates of the location of a random chosen point that is uniformly distributed in a region. Given Y = 1, find the expected value of X when the...

Let (X, Y) be uniformly distributed in the circle of radius 1 centered at the origin. Its joint density is thus Let R = (X 2 + Y 2 ) 1/2 and = tan -1 (Y/X) denote the polar coordinates of (X, Y)....

When did the term sociology coined? A.1732 B.1650 C.1838 D.1836

During the month of May 2022, Kingsway Ltd's employees earned total salaries and wages of $50,000. Payroll deductions were $3,500 for PAYG withheld tax and $2,500 for superannuation. Assume that...

If, in a sample of n = 16 selected from a left-skewed population, X = 65, and S = 21, would you use the t test to test the null hypothesis H0 : m = 60? Discuss.

4. What is a business plan? Why is studying the business plan important when considering a business venture investment?

Answer Problem 6.70 for level 2 to baseline? Data Set NIFED.DAT (at www.cengagebrain.com) was described earlier. We wish to look at the effect of each treatment separately on heart rate and systolic...

Answer Problem 6.70 for level 3 to baseline? Data Set NIFED.DAT (at www.cengagebrain.com) was described earlier. We wish to look at the effect of each treatment separately on heart rate and systolic...

Answer Problem 6.70 for the last available level to baseline? Data Set NIFED.DAT (at www.cengagebrain.com) was described earlier. We wish to look at the effect of each treatment separately on heart...

prepare an alphabetical list of all Economics majors that entered the university in 2 0 2 1 the list should only display first and last names

What's the taxable equivalent yield on a municipal bond with a yield to maturity of 6.25 percent for an investor in the 25 percent marginal tax bracket? (Round your answer to 2 decimal places.)...

Foreign Cars List Price in K Sale Price in K Days to Sell Total 9445.6 8966.0 11252.0 Mean 47.2 44.8 56.3 Median 49.0 45.4 53.0 Range (Max-Min) 87.3 87.1 102.0 St.Dev 26.0993 26.0304 30.9969 Co.Eff....