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5.61 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the unit circle C = {(x, y): x² + y² ≤ 1}? 5.62 What in Gaignt of the Cartesian coordinates of a

5.61 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the unit circle C = {(x, y): x² + y² ≤ 1}? 5.62 What in Gaignt of the Cartesian coordinates of a

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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question number 5.61

(a) Is the correlation coefficient of the rates of return on the stocks A and B positive or negative? (b) How can you divide the investment amount between two stocks if you desire a portfolio with a minimum variance? What are the expected value and standard deviation of the rate of return on this portfolio? 5.60 The continuous random variables X and Y have joint density function f(x,y) = 6(x - y) for 0 < y <x< 1 and f(x, y) = 0 otherwise. What is the correlation coefficient of X and Y? 5.61 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the unit circle C = {(x, y): x² + y² ≤ 1}? 5.62 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the region D = {(x, y): [x] + [y] ≤ 1}? 5.63 Suppose that (X, Y) is a random point inside the unit square {(x, y): 0 ≤ x,y ≤ 1). What is the correlation coefficient of the random variables V = min (X, Y) and W = max(X, Y)? 1
Transcribed Image Text:(a) Is the correlation coefficient of the rates of return on the stocks A and B positive or negative? (b) How can you divide the investment amount between two stocks if you desire a portfolio with a minimum variance? What are the expected value and standard deviation of the rate of return on this portfolio? 5.60 The continuous random variables X and Y have joint density function f(x,y) = 6(x - y) for 0 < y <x< 1 and f(x, y) = 0 otherwise. What is the correlation coefficient of X and Y? 5.61 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the unit circle C = {(x, y): x² + y² ≤ 1}? 5.62 What is the correlation coefficient of the Cartesian coordinates of a random point (X, Y) inside the region D = {(x, y): [x] + [y] ≤ 1}? 5.63 Suppose that (X, Y) is a random point inside the unit square {(x, y): 0 ≤ x,y ≤ 1). What is the correlation coefficient of the random variables V = min (X, Y) and W = max(X, Y)? 1
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