Prove that if the joint cdf of X and Y satisfies Fx,y(x,y) = FX(X)FY(y), then for any

Question:

Prove that if the joint cdf of X and Y satisfies
Fx,y(x,y) = FX(X)FY(y),
then for any pair of intervals (a, b), and (c, d),
P(a < X < b, c < Y < d) = P(a < X < b)P(c < Y < d).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:20 AM

See More Questions

Prove that if |f(x)| Then lim g(x) = 0. lim f(x)g(x) = 0.
A pdf is defined by (a) Find the value of C. (b) Find the marginal distribution of X. (c) Find the joint cdf of X and Y. (d) Find the pdf of the random variable Z = 9/(X + l)2. +2y) if 0 < <1 and 0 2...
Prove that if the initial velocity satisfies = b e corng A, then the solution to the initial value problem (9.65, 71) remains bounded. (to)
Suppose that, in a Brazilian municipality, theprobability that a randomly selected resident likessoccer is 1/4, while the probability that he likes soap operas is1/2. Determine the probability that 1...
Welch issues bonds dated January 1, 2011, with a par value of $250,000. The bonds annual contract rate is 9%, and interest is paid semiannually on June 30 and December 31. The bonds mature in three...
Simplex Corporation provides the following information at the end of 2015. Salaries payable to workers at the end of the year ................ $ 3,500 Advertising expense for the year...
As the marketing manager for Smart Fones Industries Pty Ltd you have asked the accountant what it costs to make the SFI2026 model as you want to set a price for the phone. A similar phone produced by...
Maria Lorenzi owns an ice cream stand that she operates during the summer months in West Yellowstone, Montana. Her store caters primarily to tourists passing through town on their way to Yellowstone...
Discuss the principles of process intensification (PI) and its role in achieving sustainable and efficient chemical processing, focusing on the reduction of equipment size, energy consumption, and...
The small cart has a speed v A = 4 m /s as it passes point A. It moves without appreciable friction and passes over the top hump of the track. Determine the cart speed as it passes point B. Is...
A woman leaves for work between 8 AM and 8:30 AM and takes between 40 and 50 minutes to get there. Let the random variable X denote her time of departure, and the random variable Y the travel time....
Color blindness appears in 1% of the people in a certain population. How large must a sample be if the probability of its containing a color-blind person is to be .95 or more? (Assume that the...
The state-space representation of a system model is described as where Find a. The I/O equation. b. The transfer function. (x = Ax+ Bu y=Cx+Du
Solve. x+3x-22x-7 The solution set is
Solve the equation. 2y 8y y-6 y-6
An organization is releasing a major application within the next 60 days. The organization asked an auditor to do an assessment. The auditor has insufficient time to review all of the controls but is...
What are some problems that can arise from strategic decisions made by the board of directors? 1 point
A company that sells its product in a foreign market below the cost of production may be accused of what?
Falk Enterprises borrowed $8500 at 6.25% compounded semiannually to purchase a new forklift. The loan agreement stipulates regular semiannual payments be made over the next three years. Prepare the...
Independent random samples of sizes n1 = 30 and n2 = 50 are taken from two normal populations having the means 1 = 78 and 2 = 75 and the variances 21 = 150 and 22 = 200. Use the results of Exercise...
The data from 200 machined parts are summarized as follows: Depth of bore Above Below Edge condition Target Target Coarse 15 10 Moderate 25 20 Smooth 50 80 (a) What is the probability that a part...
Computers in a shipment of 100 units contain a portable hard drive, CD RW drive, or both according to the following table: Portable hard drive Yes No CD RW Yes 15 80 No 4 1 Let A denote the events...
The probability that a customers order is not shipped on time is 0.05. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be...
With regard to the production possibilities frontier (PPF), an efficient point is a point that is: ?
Within the context of rapidly evolving regulatory landscapes and heightened ethical scrutiny, how do advanced organizations navigate the ethical complexities of technological innovation and...
Write a program that accepts an integer limit and an integer value and that prints a complete line of output reporting the multiples of value uptil the limit . Keep prompting the user for a value...

Prove that if the joint cdf of X and Y satisfies Fx,y(x,y) = FX(X)FY(y), then for any

Question:

Step by Step Answer:

Pa X b c Y d PX b c Y d PX a c Y d PX b Y d PX b Y c ...View the full answer

Statistical Inference

Students also viewed these Statistics questions