Question: Consider Review Exercise 3.66. There are two service lines. The random variables X and Y are the proportion of time that line 1 and line

Consider Review Exercise 3.66. There are two service lines. The random variables X and Y are the proportion of time that line 1 and line 2 are in use respectively. The joint probability density function for (X, Y) is given by?

(a) Determine whether or not X and Y are independent.

(b) It is of interest to know something about, the proportion of Z = X 4 ? Y. the sum of the two proportions. Find E(X + Y). Also find E (XY).

(d) Find Var(X + Y).

+ y), 0 < r, y 1. elsewhere. S(a, y)

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a gx fx y dy 3x 1 for 0 x 1 and hy 3y 1 for 0 y 1 Since fx y ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

18-M-S-E (75).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

A legitimate concern about illegal immigration is that it tends to lead to higher product prices. has a negative fiscal impact on local and state governments. causes a one-for-one reduction in...

The random variables X and Y in Exercise 2, with variances found in Section 7.2, Exercise 10. For the following joint distributions, find the probabilities for the random variable X - Y (the...

The random variables X and Y in Exercise 3, with variances found in Section 7.2, Exercise 11. For the following joint distributions, find the probabilities for the random variable X - Y (the...

A solid uniform ball rolls without slipping up a hill, as shown in (Figure 1). At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff. Neglect rolling friction...

solve these practice problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used...

4.70 Consider Review Exercise 3.64 on page 127. There are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint...

Consider Review Exercise 3.64 on page 127. There are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability...

solve these practice problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used...

solve these problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used for a...

MEAN 6.0000 WHEN WE HAVE LARGE DATA SETS, WE GROUP THE DATA. IN THIS CASE OUR GROUPS WILL BE: STD DEV 2.17 IN A NORMAL DISTRIBUTION THE MEAN, MEDIAN AND MODE ARE ALL THE SAME NUMBER X-VALUES Z-VALUES...

For each transaction, indicate the amount of the cash flow, indicate whether each results in an inflow or outflow of cash, and give the section of the statement in which each cash flow would appear....

The McDonald Group is purchasing a piece of property for $1.2 million. Two finance companies offer McDonald different loan terms to finance the purchase. Finance company A requires McDonald to put a...

Why is risk assessment the balancing of the potential for loss against the cost of controls?

Suppose that people consume only three goods, as shown in this table: a. What is the percentage change in the price of each of the three goods? b. Using a method similar to the consumer price index,...

Paulson Winery in Albany, New York, has two departments: Fermenting and Packaging. Direct materials are added at the beginning of the fermenting process (grapes) and at the end of the packaging...

Stowe Enterprises owns the following assets at December 31, 2008. Cash in bank-savings account . 63,000 Checking account balance .... 17,000 Cash on hand ........ 9,300 Postdated checks ........ 750...

The residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2010, they buy 100 heads of cauliflower for $200, 50 bunches of broccoli for $75, and 500 carrots for $50....

Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State Probability Return Fast growth Slow growth Recession...

Find the critical points and apply the Second Derivative Test (or state that it fails). (x) = sin 2 x + cos x, [0, ]

Refer to Exercise 20. You have a random sample of 100 population members from each of two populations. You intend to use sample results to test the following hypotheses: H 0 : 1 2

A study conducted at the University of Chicago Hospitals compared the hospital related performance of hospitalists physicians specializing in caring for hospitalized patients to the performance of...

The Boulder Fire Department conducted a study of average emergency response times for its two stations. For a sample of 125 emergency responses by the North Boulder Station, average response time was...

Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2,580,000. The fixed asset will be depreciated straight-line to zero over its...

Question: A researcher wishes to determine whether people with high blood pressure can reduce the blood pressure by following diet. Use a significance level of 0.01 to test the claim that the...

Hi, I need your help with these questions, thanks Please use R studio if apply 1) You are employed at a large agricultural company. This company produces two species of grass, and would like to know...