Mean and Variance - Covariance
Not what you're looking for?
See attached file for full problem description.
1. Assume that there are 5 states of the world, s = 1, ..., 5. Suppose that the probabilities are given by pi_1 = pi_2 = pi_3 = 0.1, pi_4 = 0.35, pi_5 = 0.35.
Consider three random variables (x(s), y(s), z(s))^2_s-1, which are defined as follows.
X(A) = 1, x(2) = 2, x(3) = 3, x(4) = 4, x(5) = 5
y(1) = 1, y(2) = 0, y(3) = 1, y(4) =0, y(5) = 1
z(1) = 0, z(2) = 1, z(3) = 0, z(4) = 1, z(5) = 0.
a) Compute the mean and the variance of each of these three random variables, i.e. compute E(x), E(y), E(z) as well as var(x), var(y), var(z).
b) Compute all covariances, i.e. compute cov(x,y), cov(x,z) and cov(y,z).
c) Define a new random variable
w_1(s) = y(s) + z(s) , s = 1, ..., 5.
Compute the variance of w_1. Compute the covariance between w_1 and y.
d) Define a new random variable
w_2(s) = x(s) + 2y(s) + z(s) , s = 1, ..., 5
Compute the variance of w_2. Compute the covariance between w_2 and x, between w_2 and z and between w_2 and w_1.
Purchase this Solution
Solution Summary
This post shows the calculations for covariance of every pair.
Purchase this Solution
Free BrainMass Quizzes
Economic Issues and Concepts
This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.
Elementary Microeconomics
This quiz reviews the basic concept of supply and demand analysis.
Basics of Economics
Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.
Economics, Basic Concepts, Demand-Supply-Equilibrium
The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.
Pricing Strategies
Discussion about various pricing techniques of profit-seeking firms.