Question: Suppose that a r.vec. X = (X 1 ,X 2 ) has the distribution uniform on the circle (not a disk!) x 2 1 +x

Suppose that a r.vec. X = (X₁,X₂) has the distribution uniform on the circle (not a disk!) x²₁ +x²₁ = r₂ for a fixed r. This means that the vector X takes values (x₁,x₂) only from the circle mentioned, and the probability that a value of X will fall into an arc of the circle is equal to the length of this arc divided by the length of the whole circle.
Show that the distribution of the r.vec. X is not absolutely continuous; that is, the probability density function does not exist. Show that, nevertheless, the distribution of X may be identified with a one-dimensional uniform distribution. On which interval?

Step by Step Solution

★★★★★

3.50 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose that a joint density fx exists and denote by C the circle on which the distribution is ... 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 And Stochastic Modeling Questions!

KEEPING IT REAL SUAREZ COMPUTER CENTER In preparing for next year, on December 1, Troy Falco hired two hourly employees to assist with some troubleshooting and repair work. More information: Dec. 7...

The following data relate road width x and accident frequency y. Road width (in feet) was treated as the independent variable, and values y of the random variable Y, in accidents per 108 vehicle...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Two independent threads are run on different processors in a chip-multiprocessor. Each thread simply increments a private counter one million times. The two counters are stored in consecutive memory...

1. A fair coin is tossed 10 times. What is the probability that exactly 6 heads will occur. 2. If 3% of the electric bulbs manufactured by a company are defective find the probability that in a...

Control Theory allows us to find various useful properties of a system such as stability. Draw a picture of a generic control system, explaining the functions of feedback and the design goals for the...

ANS 0 Question 17 v The random variable is two more than the numtler'g/f 2'5 facing on the dice. You roll three colored dice: Give the random variable. 11V. : > Next Question 0 Question 10 v In a...

s 1. Find the center of mass of the following plane region with variable density. Describe the distribution of mass in the region: The upper half (y 0) of the y 2 2 disk bounded by the circle x + y...

Homework 2 1. In this question you'll explore some pieces of density estimators. (a) First consider the kernel functions: calculate K2 for the uniform, Epanechnikov, biweight and Gaussian kernels....

(a) Show, by conserving momentum and energy, that it is impossible for an isolated electron to radiate only a single photon. (b) With this result in mind, how can you defend the photon exchange...

On January 1, 2017, Eddy Corporation had retained earnings of $650,000. During the year, Eddy had the following selected transactions. 1. Declared cash dividends................... $120,000. 2....

Which of the following statements concerning the calculation of the generation - skipping transfer tax ( GSTT ) is CORRECT? The GSTT is determined by multiplying the taxable amount by the applicable...

Include product reviews. Ninety-two percent of online shoppers read online reviews, and 88 percent of shoppers say that reviews influence their purchase decisions. Including product reviews produces,...

If you were a nonprofit CEO and were approached by another nonprofit CEO about the possibility of collaborating, what are some of the first questions you might have?

If you were a nonprofit CEO, what concerns might you have about collaborating with a local government agency?

Read the article, Nonprofit Public Collaborations: Understanding Governance Dynamics by Cornforth, Hayes, and Vangen. (See Articles.)What do the authors mean by the term collaborative windows?...

Which type of graph is commonly used for modeling dependencies between tasks in project management? A . Directed graph B . Weighted graph C . Undirected graph D . Bipartite graph

If you invested $1,500 in a stock today and it earned an 13% return in each of the next three years, then the value of the stock at the end of three years would be closest to: $2,234. $2,074. $2,164....

Alicia owns 100 shares of Gutierrez common stock with a basis of $15,000 and a $40,000 FMV. She receives 100 stock rights with a total FMV of $10,000. Alicia decides to sell the stock rights for...