Suppose (X, Y) are distributed uniformly on the circle of radius 1 centered at the origin. Find
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 X and Y independent?
Step by Step Answer:
The area of the circle is so fx y 1 where 1 ...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics 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...
-
Direct Materials Budget The MSC Company has anticipated its unit sales for the first half of 2022 as follows: 2022 Units January 12,000 February 14,000 March 15,000 16,000 17,000 18,000 April May...
-
Stretch a piece of balloon rubber not too tightly over a radio loudspeaker. Glue a small, very lightweight piece of mirror, aluminum foil, or polished metal near one edge. Project a narrow beam of...
-
Refer to the information in E19.16 and assume Opsco Corp. applies IFRS. Instructions Complete a post-retirement work sheet for 2020, and prepare all required journal entries related to the plan made...
-
Water flows by gravity from one lake to another as sketched in Fig. P5.113 at the steady rate of \(80 \mathrm{gpm}\). What is the loss in available energy associated with this flow? If this same...
-
Go to the Structural Styles section and create a style rule that sets the background color of the browser window to rgb(173, 189, 227). Create a style rule for the body element that sets the...
-
1. Identify a specific business that uses Artificial Intelligence and Robotics. 2. Why did you select this organization for your research project? 3. Identify three major issues for the use of...
-
A molded plastic product (p = 1200 kg/m 3 c = 1500 J/kg K, k = 0.30 W/m K) is cooled by exposing one surface to an array of air jets, while the opposite surface is well insulated. The product may...
-
Suppose X and Y are i.i.d. exponential random variables with = 1. Find the density of X/Y and use it to compute P(X/Y < 1).
-
Suppose X and Y have joint probability density f(x, y) = g(x)h(y) for some functions g and h which depend only on x and y, respectively. Show that X and Y are independent with fX(x) g(x) and fY(y) ...
-
Include the directrix that corresponds to the focus at the origin. Label the vertices with appropriate polar coordinates. Label the centers of the ellipses as well. 12 3 + 3 sin 0
-
Q1 (25 points) FMC Corporation, an American chemical manufacturing company headquartered in Philadelphia, Pennsylvania is considering acquisition of Cheminova, a European crop protection player. FMC...
-
The declining-balance method of depreciation is an accounting method businesses use to deduct most of the cost of new equipment during the first few years of purchase. Unlike other methods, the...
-
The price and market capitalizations of Intel, Microsoft, NIKE, and Alphabet are listed as follows. Intel: $47.60/Share: Market Cap = $188.7 billion Microsoft: $305.40/Share: Market Cap = $2.2...
-
Describes a situation that has persisted to some extent over the last three years. How did the riskier labor markets react? Did we see wage adjustments of the sort predicted by the theory of...
-
Given the data below answer the question. Account | Debit | Credit Cash | 5,600 | Accounts Receivable|1,170 | Supplies | 450 | Equipment |5,580 | Accounts Payable | | 2230 Notes Payable | | 1,800...
-
Over the next 100 years, real GDP per capita in Groland is expected to grow at an average annual rate of 2.0%. In Sloland, however, growth is expected to be somewhat slower, at an average annual...
-
Determine the annual percentage yield for a loan that charges a monthly interest rate of 1.5% and compounds the interest monthly.
-
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...
-
Include your strategies for capitalizing on your strengths and overcoming your weaknesses in order to become successful in your work related goals
-
when Recognizing and Identifying Child Abuse and Neglect, Include some strategies for capitalizing on strengths and overcoming weaknesses in order to become successful in your work-related goals?
-
What can be the most beneficial when learning about Recognizing and Identifying Child Abuse and Neglect? How can Recognizing and Identifying Child Abuse and Neglect will assist you in achieving...
Study smarter with the SolutionInn App