Question

Reduce the following expectations to linear combinations of
constants and the following terms µX, µY ,

σ2 X, σ2 Y , and σXY . Do not leave expectation operators.

i) E[5(X + Y)−(X −µX)(Y −µY)]

ii) E[2(X −µX)^2 + (Y −µY)^2 + 5]

iii) Variance (3X + Y).

Answer #1

1a) Find all the integer solutions of each of the following
linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 15x + 18 y =17.
1b) Find all solutions in positive integers of each of the
following linear Diophantine equations:
(i) 2x + y = 2,
(ii) 3x - 4y = 0,
and
(iii) 7x + 15 y = 51.

Let X and Y be two independent random variables with
μX =E(X)=2,σX =SD(X)=1,μY =2,σY =SD(Y)=3.
Find the mean and variance of
(i) 3X
(ii) 6Y
(iii) X − Y

The expected values, variances and standard Deviatiations for
two random variables X and Y are given in the following table
Variable
expected value
variance
standard deviation
X
20
9
3
Y
35
25
5
Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.
E(X+10) = ,
StDev(X+10) =
E(2X) = ,
StDev(2X) =
E(3X-2) = ,
StDev(3X-2) =
E(3X +4Y) = ,
StDev(3X+4Y) =
E(X-2Y) = ,
StDev(X-2Y) =

Linear Combinations
2)
Returns on stocks X and Y are listed below:
Period 1 2 3 4 5 6 7
Stock X 4% 7% -2% 40% 0% 10% -1%
Stock Y 2% -5% 7% 4% 6% 11% -4%
Consider a portfolio of 10% stock X and 90% stock Y.
What is the mean of portfolio returns?
Please specify your answer in decimal terms and round your
answer to the nearest thousandth (e.g., enter 12.3 percent as
0.123).
3)
Returns on...

Find the values of a and b for which the following system of
linear equations is (i) inconsistent; (ii) has a unique solution;
(iii) has infinitely many solutions. For the case where the system
has infinitely many solutions, write the general solution.
x + y + z = a
x + 2y ? z = 0
x + by + 3z = 2

A discrete time system can be
i. Linear or non-linear
ii. Time invariant or Time Variant
iii. Causal or noncausal
iv. Stable or unstable
v. Static Vs Dynamic
Examine the following systems with respect to every property
mentioned above and give a brief
explanation.
a. y[n] = x[n]δ[n − 1]
b. y[n] = x[n] + nu[n + 1]
c. y(n) = x(2. n)
d. y(n) = 3. x(n)

Decide whether or not the following equations are linear:
(a) d^2/dx^2y(x) = -8(y(x))^2 is a
- linear equation
- non-linear equation
(b) d/dx(yx) + sin(4y) = 0 is a
- linear equation
- non-linear equation
(c) sin(8x)*d/dxy(x) + y(x) = 7x is a
- linear equation
- non-linear equation
(d) d/dtx(t) +3x = -8t^3 is a
- linear equation
- non-linear equation
(e) sin(5y(x))d/dxy(x) + y(x) = 9x is a
- linear equation
- non-linear equation

Consider the following statements.
(i) The differential equation y′ + P(x) y = Q(x) has the form
of a linear differential equation.
(ii) All solutions to y′ = e^(sin(x^2 + y)) are increasing
functions throughout their domain.
(iii) Solutions to the differential equation y′ = f (y) may
have different tangent slope for points on the curve where y = 3,
depending on the value of x

Complete steps (i)-(vii) below in order to estimate the
following values using linear approximation: (a) cos(31π/ 180) (i)
Identify the function, f(x). (ii) Find the nearby value where the
function can be easily calculated, x = a. (iii) Find ∆x = dx. (iv)
Find the linear approximation, L(x). (v) Compute the approximate
value of the expression using the linear approximation. (vi)
Compare the approximated value to the value given by your
calculator. (vii) Compare dy and ∆y using the value...

Let X and Y be jointly distributed random variables with means,
E(X) = 1, E(Y) = 0, variances, Var(X) = 4, Var(Y ) = 5, and
covariance, Cov(X, Y ) = 2.
Let U = 3X-Y +2 and W = 2X + Y . Obtain the following
expectations:
A.) Var(U):
B.) Var(W):
C. Cov(U,W):
ans should be 29, 29, 21 but I need help showing how to
solve.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 33 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago