Let fX,Y (x, y) = 2e(x+y), 0 x, 0 y. Show that X and Y

Question:

Let fX,Y (x, y) = λ2e−λ(x+y), 0 ≤ x, 0 ≤ y. Show that X and Y are independent. What are the marginal pdfs in this case?

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Mathematical Statistics And Its Applications

ISBN: 9780321693945

5th Edition

Authors: Richard J. Larsen, Morris L. Marx

See More Books

Question Posted: Dec 20, 2015 03:23 AM

See More Questions

Let X, Y have joint density fX, Y(x, y) = x + y, for 0 x,y 1, and fx, y (x, y) = 0 otherwise. Find the joint CDF, i.e., Fx, y (x, y) = P(X x, Y y).
Let X, Y, Z have joint density fX,Y,Z (x,y,z) = 6, for 0 < x < y < z < l and fX,Y,Z (x,y,z) = 0 otherwise. a. Are X and Y and Z independent? b. Find the density fX(x) of X. c. Find the density fY(y)...
Let X,Y have joint density fX,Y (x, y) = 3x,y/1250, for 0 x, 0 y, x + y 10 and fX,Y(x,y) = 0 otherwise. a. Are X and Y independent? b. Find the density fx(x) of X. c. Find the density fy(y) of Y.
Ruby works in the treasury department of a large airline company. Over the coming months the airline company expects to increase flights as countries continue to ease travel restrictions. Ruby and...
(a) By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b) Select two points from the scatter diagram and nd the equation of the line containing...
Early in its 2014 fiscal year (December 31 year end), Hayes Company purchased 10,000 shares of Kenyon Corporation common shares for $26.18 per share, plus $1,800 in brokerage commissions. These...
Assign state numbers to the states in the traffic light example of Exercise B.41 and use the tables of Exercise B.42 to write a set of logic equations for each of the outputs, including the...
An HMO has just proposed an offer to promote your facility as the region's "Center of Excellence" for obstetrical deliveries. The HMO covers 700,000 lives in the community served by your facility....
ABC Company is preparing its Selling and Administrative Expense budget. ABC Company predicts sales as follows: ABC Company has prepared the following list of expected operating expenses: - $2,600...
One of Martys partners, Ann, has organized information on lead times, inventory on hand, and lot- sizing rules (established by suppliers): Scheduled receipts are After the dot-com business he tried...
The four random variables W, X, Y, and Z have the multivariate pdf fW,X,Y,Z(w, x, y, z)=16wxyz For 0
Find c if fX,Y (x, y)= cxy for X and Y defined over the triangle whose vertices are the points (0, 0), (0, 1), and (1, 1).
During March, the Wessue Coffee Emporiums employees earned wages of $18,000. Social security (FICA) withheld was $1,377; federal income taxes withheld were $3,600; and employees contributions to the...
Companies in the tire manufacturing business use a lot of property, plant, and equipment. Tyrell Rubber and Tire Corporation and Maxwell Rubber and Tire Manufacturing are two of the leading...
(7%) Problem 11: A student launches a small rocket which starts from rest at ground level. At a height h = 2.09 km, the rocket reaches a speed of v = 291 m/s. At that height, the rocket runs out of...
2. For the following three sets of electric field lines, what charge or charges would make such lines? Indicate their locations and type of charge (e.g. positive/negative) a.
What is the most important take-home point that you learned from this video? https://www.youtube.com/watch?v=nUZqvsF_Wt0 2. Policy Problems. What is onepolicy that creates inequality in the labor...
An employee had $20,300 in gross earnings up to September 20, 2021. She has the following information for her pay for the week ending September 27, 2021. Her employer contributes 100% toward CPP and...
To what extent may a corporation accumulate earnings for the reasonable needs of a related corporation? To what extent does it matter that the following conditions prevail? a. A parent-subsidiary...
Do animals have rights? If so, what are they? What duties do human beings have toward animals? Does KFC protect animal welfare at an acceptable level?
Why is a broad background essential for the project manager? What is a broad background?
In roulette, a wheel with 38 numbers is spun. Of these, 18 are red, and 18 are black. The other two numbers, which are neither black nor red, are 0 and 00. The probability that when the wheel is spun...
Which is more likely: rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled?
Explain what is wrong with the statement that in the Monty Hall Three-Door Puzzle the probability that the prize is behind the first door you select and the probability that the prize is behind the...
You borrowed $15,000 for buying a new car from a bank at an interest rate of 12% compounded monthly. This loan will be repaid in 48 equal monthly installments over four years. Immediately after the...
Discuss how debt restructuring, settlement, or modification works. Discuss the journal entries for debtor and creditor
Could CNL be a viable business? If so, under what conditions and what level of production (and, since production is directly related to production workers, employees)? All information provided for...

Let fX,Y (x, y) = 2e(x+y), 0 x, 0 y. Show that X and Y

Question:

Step by Step Answer:

The marginal pdfs for f X Y are f X x e x and f Y y e y Their pro...View the full answer

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions