Suppose X and Y are independent random variables. Ya. What is the correlation coefficient of X and X – Y? Your answer will be in terms of var(X)and υar (Y).b. What is the conditional expectations of E[(X –Y)|X] and E[(X – Y)²|X]? You answer couldbe in terms of X,Y, E(X), E(X²), E(Y), and E(Y²).

Answered: Image /qna-images/answer/91e4fad1-2a00-4d65-aefa-62b2738dcde4.jpg

Answered: Suppose X and Y are independent random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the correlation r between two quantitative variables was found to be r = 0. This means that: O (a) there is a strong linear relationship between the two variables. O (b) there is no linear relationship between the two variables. (c) there is a strong relationship between the two variables. (d) there is no relationship between the two variables. (e) none of the above.
Two independent variables x and y have means 5 and 10 and variances 4 and 9 respectively. Find the coefficient of correlation between u and v where (i) u = 3x + 4y: v = 3x - y %3D (ii) If x and y are not independent and r - •5, u - x + y.
For an experiment, roll 2 fair dice. Let the random variables, X = sum of the 2 dice Y = larger value - smaller value (if the 2 dice are the same value, let Y =0) (a) Find the mean and variance of W1 = 2x-3y (b) Find the covariance between W1 and W2 = x + y
(d) The Var(x + y) = 1.4979. Compute the covariance of x and y. What can you say about the relationship between quality and meal price? Is this what you would expect? (e) Compute the correlation coefficient between quality and meal price. What is the strength of the relationship? Do you suppose it is likely to find a low-cost restaurant in this city that is also high quality? Why or why not?
1,3,4
3.Find the population variance or covariance given each scenario below:
8(23). Two balanced dice are thrown. Let X be the outcome on the first die and Y the outcome on the second. If Z = X + Y, find the correlation between X and Z.
A scientist wants to develop a model to describe the relationship between the average daily temperature, x °C, and her household’s daily energy consumption, y kWh, in winter. A random sample of the average daily temperature and her household’s daily energy consumption are taken from 10 winter days and shown in the table. x -0.4 -0.2 0.3 0.8 1.1 1.4 1.8 2.1 2.5 2.6 y 28 30 26 25 26 27 26 24 22 21 You may use: Sy=255 Sxy=283.8 Syy= 64.5 Find a value for the product moment correlation coefficient r for this data Explain what the value of the product moment corelation tells you about the relationship between daily temperature and the household energy consumption.
Give an explanation why this statement is either true or false: Portfolio contains n assets. Therefore, portfolio variance for this portfolio is the function of 2n covariances and n variances.
1. Suppose a X value is produced by a random process that has a mean of 1 and a variance of 9, while a Y value is produced by a random process that has a mean of 9 and a variance of 1. Let Z = 3X - 2Y. Compute: a. the mean and variance of Z assuming X and X are independent. b. the mean and variance of Z assuming X and X are not independent and their correlation coefficient is 0.50.
Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?
Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is either +1 or −1. State the conditions which make the correlation equal to +1.

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