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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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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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