If a random variable V is independent of two independent random variables X and Y, prove that

Question:

If a random variable V is independent of two independent random variables X and Y, prove that V is independent of X + Y.

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 03:24 AM

See More Questions

If X, Y, and Z are independent random variables having identical density functions f(x) = ex, 0 < x < , derive the joint distribution of U = X + Y, V = X + Z, W = Y + Z.
If X and Y are independent random variables with variances 2x = 5 and at = 3, find the variance of the random variable Z = 2X + 4Y 3.
Independent random variables X and Y have the means and standard deviations as given in the following table. Use these parameters to find the expected value and SD of the following random variables...
A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18s. What is...
Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The following...
Two conventional CD triaxial compression tests were conducted on a dense angular dry sand at the same void ratio. Test A had a confining pressure of 150 kPa, while in test B the confining pressure...
Following data refers to a test on a petrol engine. Indicated power $=30 \mathrm{~kW}$, Brake power $=26$ $\mathrm{kW}$, Engine speed $=1800 \mathrm{RPM}$, Brake specific fuel consumption...
A, B, C, D, and E constituted the board of directors of the X Corporation. While D and E were out of town, A, B, and C held a special meeting of the board. Just as the meeting began, C became ill. He...
Westgaard Incorporated uses a job-order costing system and its total manufacturing overhead applied always equals its total manufacturing overhead. In March, the company completed job G87M that...
Bank Beta has an inventory of AAA-rated, zero-coupon bonds with a maturity of 13.42 years and a face value of $127,503,041. The modified duration of these bonds is 12.5 years, the DEAR is $2,150,000,...
Let X and Y be two independent random variables, whose marginal pdfs are given below. Find the pdf of X + Y. (Consider two cases, 0 w < 1 and 1 w 2.) fX(x) = 1, 0 x 1, and fY(y) = 1, 0 y 1
Let Y be a continuous nonnegative random variable. Show that W = Y2 has pdf fW(w) = 1/2w fY(w).
Evaluate the definite integrals in Problem. 3 | 36z dz
How does linear programming support decision-making in quality control and process improvement initiatives in operations management?
A 1.40 kg sample of water at 13.0C is in a calorimeter. You drop a piece of steel with a mass of 0.340 kg at 200C into it. After the sizzling subsides, what reasonable assumptions that any steam...
How does lean production impact product design and development processes?
1. How does an assessment of marketing environment forces assist in marketing opportunity analysis? 2. What are the main causes of the opening of strategic windows? 3. How can a business instigate...
How does process technology enable efficient production planning and scheduling in the supply chain?
Match the parabolas with the following equations: x 2 = 2y, x 2 = -6y, y 2 = 8x, y 2 = -4x. Then find each parabolas focus and directrix. y X
Name some of the various types of financial intermediaries described in the chapter and indicate the primary reason(s) each was created.
Let X be a random variable on a sample space S. Show that V (aX + b) = a2V (X) whenever a and b are real numbers.
A player in the Powerball lottery picks five different integers between 1 and 59, inclusive, and a sixth integer between 1 and 39, which may duplicate one of the earlier five integers. The player...
Suppose that at least one of the events Ej , j = 1, 2, . . . , m, is guaranteed to occur and no more than two can occur. Show that if p(Ej) = q for j = 1, 2, . . . , m and p(Ej Ek) = r for 1 j < k ...
What logic gate does this represent (reduce it) Do D
What basic logic gate does this implement? a b in out Not otb E in Not O out nota And out aAndNotb out Or out b notAndb a out And b
Design a Fuzzy system to reduce effect of impulse noise on a noisy image with intensities ranging from [0, L-1]. Let zs denotes the intensity of middle pixel of the neighborhood. The output intensity...

If a random variable V is independent of two independent random variables X and Y, prove that

Question:

Step by Step Answer:

Consider the continuous case It suff...View the full answer

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions