Consider a pair of random variables X, Y with constant joint density on the triangle with vertices

Question:

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices at (0, 0), (3, 0), and (0, 3).
a. Find the expected value of the sum of X and Y, i.e., find E(X + Y).
b. Find the variance of X, i.e., find Var (X).

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Probability

ISBN: 978-0716771098

1st edition

Authors: Mark Daniel Ward, Ellen Gundlach

See More Books

Question Posted: Mar 14, 2016 06:43 AM

See More Questions

Consider a pair of random variables X, Y with joint density fX,Y(x, y) = 8e-2x-4y, for 0 < x,0, < y, And fX,Y (x, y) = 0 otherwise. Find P(X 4,Y 8).
The joint density function for a pair of random variables X and Y is (a) Find the value of the constant C. (b) Find P(X 1, Y 1). (c) Find P(X + Y 1). SCx(1 + y) if 0
The joint density function for a pair of random variables X and Y is (a) Find the value of the constant C. (b) Find P(X < 1, Y < 1). (c) Find P(X + Y < 1). Cx(1 + y) if 0
Neo-Darwinism believes that new species develop through (A).Continuous variations and natural selection (B) Mutation with natural selection (C) Hybridization (D) Mutation
Refer to the level 0 DFD in Figure. Study the portion of the figure and accompanying narrative that deals with the mrp process only. Prepare a level 1 DFD for the mrp process (bubble 3.0)only. Bill...
List one possible control for each of the seven transaction-related audit objectives for acquisitions. For each control, list a test of control to test its effectiveness.
Explain how goal setting is used to motivate people. LO.1
The City of Columbia is trying to attract a new manufacturing business to the area. It has offered to install and operate a water pumping plant to provide service to the proposed plant site. This...
Thaddeus is a salaried exempt worker who earns $57,500 per year for a 45-hour workweek. During a biweekly pay period, he worked 105 hours. What is his gross pay?
Procter & Gamble has been the leading soap manufacturer in the United States since 1879, when it introduced Ivory soap. However, late in 1991, its major rival, Lever Bros. (Unilever), overtook it by...
Find the variance of the given random variable. Let X be the time, in hours, that Christine spends talking on the telephone. Then X has density fx(x) = 3e-3x, for 0 < x, and fx(x) = 0 otherwise.
Using the following probability density function a. Find the cumulative distribution function Fx(x). b. Find P(0.25 c. Find P{X > 0.45). d. Find P(X = 0.25). e. Find the mean E(X). f. Find the...
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x + 5) 2 + 4(y - 4) 2 = 16
When CH4(g) reacts with O2(g) to form CO2(g) and H2O(g), 192 kcal of energy are evolved for each mole of CH4(g) that reacts. Write a balanced equation for the reaction with an energy term in kcal as...
Ben Rogers, Judy Wilkinson, and Henry Walker were the partnership dentists. Ben Rogers became insolvent because of real estate investments. So, Judy Wilkinson and Henry Walker had to then pay the...
A random sample of 10 subjects have weights with a standard deviation of 10.8148 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
of stion 1. Harmonic Test II. Root Test III. Ratio Test Consider the series 8 = 72 Which one of the following tests can be used to determine whether it is convergent or divergent? IV. Integral Test...
Pharaoh company obtains $44,800 in cash by signing a 7%, 6 month, $44,800 note payable to First Bank on July 1. Pharoah's fiscal year ends on September 30. What information should be reported for the...
Add a class NumericQuestion to the question hierarchy of Section 9.1. If the response and the expected answer differ by no more than 0.01, accept the response as correct.
The maximum pressure that can be developed for a certain fluid power cylinder is 15.0 MPa. Compute the required diameter for the piston if the cylinder must exert a force of 30 kN.
What are the five basic steps of a presentation sales call?
For the data given in Example 8.20, find a 95% confidence interval for 2 . Again, assume that the weight is normally distributed with mean and and variance , where and are unknown. Example 8.20:...
Consider the following observed values of (x i , y i ): (1, 3), (3, 7). a. Find the estimated regression line based on the observed data. b. For each x i , compute the fitted value of y i using c....
Consider the simple linear regression model where i 's are independent N(0, 2 ) random variables. Therefore, Y i is a normal random variable with mean 0 + 1 x i and variance 2 . Moreover, Y i 's...
(International Finance) Computing a Currency changes = (e1 - e0 )/ e0 where e0 = old currency value e1 = new currency value (a) If the dinar devalues against the U.S. dollar by 45%, the U.S. dollar...
2. Fill in the time line for the Sawing Department. Use the time line to help you compute the number of equivalent units and the cost per equivalent unit in the Sawing Department for September Show...
question 6 Timely Inc. produces luxury bags. The budgeted sales and production for the next three months are as follows july. august september Sales, in units 1,115. 1229. 1302 Production. in units...

Consider a pair of random variables X, Y with constant joint density on the triangle with vertices

Question:

Step by Step Answer:

a The joint density is 29 bec...View the full answer

Introduction to Probability

Students also viewed these Statistics questions