Find the correlation coefficient between x and z

Assignment Help Advanced Statistics

Reference no: EM13550749

Question a) Consider two independent random variables X and W with identical variance. Let Y and Z be defined as

Y = aX + bW
Z = cX + dW

where a, b, c, and d are constants. Choose constants a, b, c, and d such that COV(X,Y) < 0, COV(X,Z) < 0, and COV(Y,Z) < 0. If this is not possible, provide a brief explanation why.

b) Let Z = ρX + √(1 + ρ²W), with 1 ≤ p ≤ 1. Find the correlation coefficient between X and Z.

Reference no: EM13550749

Questions Cloud

Explain an initial anesthetic of nitrous oxide : Dentists might use a mixture of 40% N2O and 60% O2 as an initial anesthetic of nitrous oxide(although exact proprtions may vary). Determine the entropy of mixing for 1 mole of such a mixture. Assume ideal gas conditions.

Estimate the angular magnification of the microscope : The eyepiece of a microscope has a focal length of 1.25 cm and the objective lens focal length is 1.26 cm. If the tube length is 17.0 cm, what is the angular magnification of the microscope

Compute the expected tree radius and its variance : Compute the expected value and variance of the ring width in a single year and compute the expected tree radius and its variance of a 50 year old tree.

Explain work is performed to remove heat from a system : A refrigerator is the reverse of an engine: work is performed to remove heat from a system, making it colder. The efficiency of a refrigerator (often termed the coefficient of performance) is defined as q3/wcycle = Tlow/(Thigh-Tlow).

Find the correlation coefficient between x and z : Find the correlation coefficient between X and Z - Consider two independent random variables X and W with identical variance.

Explain what percentage of those calories are from bicycling : Alexandra (who happens to weigh 130 pounds) has decided to start a training program bicycling for 45 minutes, 3 times/week as well as rock climbing for 1.5 hours every Saturday. How many extra calories will Alexandra burn in 8 weeks of training. W..

Estimate the fraction of electrons : Estimate the fraction of electrons excited above the fermi level at room temp for Aluminum. The effective mass of Al is 1.0xm, where m - free electron mass

Calculate the predicted quality cost savings from the design : Calculate the predicted quality cost savings from the design engineering work.

Find the expected value of the winning bid : What is the joint density of Xand Y, find the probability contractor A is awarded the iob and find the expected value of the winning bid.

User Account

All Pages