Could you help me with those tasks? I have no clue what to do ExercisesMethods25. Given below is a bivariate distribution for the random variables x and y.SELF testAx, y)25080.5330506040a. Compute the expected value and the variance for x and y.b. Develop a probability distribution for x + y.c. Using the result of part (b), compute E(x + y) and Var (x + y).d. Compute the covariance and correlation for x and y. Are x and y positively related,negatively related, or unrelated?e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the in-dividual variances? Why? 30. In addition to the information in exercise 29 on the S&P500 and core bonds, J.P. MorganAsset Management reported that the expected return for real estate investment trusts(REITS) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Manage-ment, Guide to the Markets, 1st Quarter, 2012). The correlation between the S&P 500 andREITS is .74 and the correlation between core bonds and REITS is – .04. You are consid-ering portfolio investments that are composed of an S&P 500 index fund and REITS as wellas portfolio investments composed of a core bonds fund and REITS.a. Using the information provided here and in exercise 29, determine the covariancebetween the S&P 500 and REITS and between core bonds and REITS.b. Construct a portfolio that is 50% invested in an S&P 500 fund and 50% invested inREITS. In percentage terms, what are the expected return and standard deviation forsuch a portfolio?c. Construct a portfolio that is 50% invested in a core bonds fund and 50% invested inREITS. In percentage terms, what are the expected return and standard deviation forsuch a portfolio?d. Construct a portfolio that is 80% invested in a core bonds fund and 20% invested inREITS. In percentage terms, what are the expected return and standard deviation forsuch a portfolio?e. Which of the portfolios in parts (b), (c), and (d) would you recommend to anaggressive investor? Which would you recommend to a conservative investor?Why?

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Compute the expected value and the variance for x and y. Develop a probability distribution for x + y. Using the result of part (b), compute E(x + y) and Var (x + y). Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?

Compute the expected value and the variance for x and y. Develop a probability distribution for x + y. Using the result of part (b), compute E(x + y) and Var (x + y). Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Could you help me with those tasks? I have no clue what to do

Exercises
Methods
25. Given below is a bivariate distribution for the random variables x and y.
SELF test
Ax, y)
2
50
80
.5
3
30
50
60
40
a. Compute the expected value and the variance for x and y.
b. Develop a probability distribution for x + y.
c. Using the result of part (b), compute E(x + y) and Var (x + y).
d. Compute the covariance and correlation for x and y. Are x and y positively related,
negatively related, or unrelated?
e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the in-
dividual variances? Why?

30. In addition to the information in exercise 29 on the S&P500 and core bonds, J.P. Morgan
Asset Management reported that the expected return for real estate investment trusts
(REITS) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Manage-
ment, Guide to the Markets, 1st Quarter, 2012). The correlation between the S&P 500 and
REITS is .74 and the correlation between core bonds and REITS is – .04. You are consid-
ering portfolio investments that are composed of an S&P 500 index fund and REITS as well
as portfolio investments composed of a core bonds fund and REITS.
a. Using the information provided here and in exercise 29, determine the covariance
between the S&P 500 and REITS and between core bonds and REITS.
b. Construct a portfolio that is 50% invested in an S&P 500 fund and 50% invested in
REITS. In percentage terms, what are the expected return and standard deviation for
such a portfolio?
c. Construct a portfolio that is 50% invested in a core bonds fund and 50% invested in
REITS. In percentage terms, what are the expected return and standard deviation for
such a portfolio?
d. Construct a portfolio that is 80% invested in a core bonds fund and 20% invested in
REITS. In percentage terms, what are the expected return and standard deviation for
such a portfolio?
e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an
aggressive investor? Which would you recommend to a conservative investor?
Why?

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