Question: If the random variables X and Y are related through the expression Y = aX + b show that they have a correlation of I

If the random variables X and Y are related through the expression
Y = aX + b
show that they have a correlation of I if a > 0 and of -1 if a < 0.

Step by Step Solution

★★★★★

3.29 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Notice that EY aEX b and VarY a 2 Va... View full answer

blur-text-image
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)

Word file Icon

943-M-S-P (9015).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

1. If managers believe that costs for both fuels tend to rise and fall together, then they should model X and Y as independent. 2. A negative covariance between X and Y would increase the uncertainty...

Q:

If the random variables X and Y have the joint pdf show that Cov(X, Y) = 8/450. Calculate (X, Y). fry(x,y) = 0, otherwise

Q:

The random variables X and Y have joint density function f (x, y) = 12xy(1 x) 0

Q:

1. Probability theory and mathematical statistics: if the random variables X and Y obey a two-dimensional standard normal distribution and the correlation coefficient between X and Y is . If the...

Q:

1. Probability theory and mathematical statistics: if the random variables X and Y obey a two-dimensional standard normal distribution and the correlation coefficient between X and Y is If the...

Q:

Two jointly Gaussian zero-mean random variables, X and Y, have respective variances of 3 and 4 and correlation coefficient P xy = -0.4. A new random variable is defined as Z = X + 2Y. Write down an...

Q:

(e) Suppose that the random variables X and Y are related by Y = 2 - 3X. What is the expected value of Y in terms of the expected value of X? What is the variance of Y in terms of the variance of X?...

Q:

Two random variables X and Y are exponentially distributed with respective rates Ax = 1 and Ay = 2. Now, consider flipping a fair coin and observing the value of X if the outcome of the coin flip is...

Q:

Suppose two random variables X and Y are related as follows: Y = 1/X2. The population Pearson correlation coefficient should be Multiple Choice +1. 0. 1. None of the options are correct. .5

Q:

Given a pair of random variables X and Y having the variances 21 and 22 and the correlation coefficient , use Theorem 4.14 to express var(X/s1 + Y/s2) and var(X/s1 Y/s2) in terms of 1, 2, and ....

Q:

Evaluate integrals de (a) ). - 1

Q:

A 100-70-04 nodular iron has tensile and yield strengths described by Sut = W [47.6, 125.6, 11.84] kpsi Sy = W [64.1, 81.0, 3.77] kpsi What is the chance that Sut is less than 100 kpsi? What is the...

Q:

Equivalent Units of Conversion Costs The Rolling Department of Jabari Steel Company had 2 , 8 7 7 tons in beginning work process inventory ( 2 0 % complete ) on October 1 . During October, 4 1 , 1 0...

Q:

15 Impact of reinvested foreign earnings on NPV Flagstaff Corp. is an Australia-based company with a subsidiary in China. It plans to reinvest its earnings in Chinese Government securities for the...

Q:

26. A manufacturer of capacitors claims that the breakdown voltage of these capacitors has a mean value of at least 100 V. A test of 12 of these capacitors yielded the following breakdown voltages:...

Q:

27. A sample of 10 fish were caught at lake A and their PCB concentrations were measured using a certain technique. The resulting data in parts per million were Lake A: 11.5, 10.8, 11.6, 9.4, 12.4,...

Q:

28. A method for measuring the pH level of a solution yields a measurement value that is normally distributed with a mean equal to the actual pH of the solution and with a standard deviation equal to...

Q:

Question Identify and describe a country other than the United States that you believe would be a wise addition for someone seeking portfolio diversification. This will require some time and...

Q:

10 1 point Create the probability table for the combined Houses of Congress based upon the data presented in the instructions for Case Study 2. Republican Democrat Independent Libertarian Total Male...

Q:

A single client, 64, a recently retired engineer, lives in a high income tax state. Their only income is Social Security of $31,800 per year. Living expenses are $59,000 with a mortgage payment of...