Question

f_X,Y(x,y)=xy 0<=x<=1, 0<=y<=2

f_X(x)=2x 0<=x<=1, f_Y(y)=y/2
0<=y<=2 **choose the all correct things.**

a. E[X]=1/2

b. E[XY]=8/9

c. COV[X,Y]=1

d. correlation coefficiet =1

Answer #1

a) U = xy
b) U = (xy)^1/3
c) U = min(x,y/2)
d) U = 2x + 3y
e) U = x^2 y^2 + xy
2. All homogeneous utility functions are homothetic. Are any of
the above
functions homothetic but not homogeneous? Show your work.

Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2,
and E[X2]=E[Y2]=E[Z2]=5.
Find cov(XY,XZ).
(Enter a numerical answer.)
cov(XY,XZ)=
Let X be a standard normal random variable. Another random
variable is determined as follows. We flip a fair coin (independent
from X). In case of Heads, we let Y=X. In case of Tails, we let
Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not...

differential equation one solution is given,
xy''-(2x+1)y'+(x+1)y=x^2; y_1=e^x

a. Finish the probability table
b. DefineY =−2X+6.CalculateE(X),Std(X),E(Y),Std(Y),Cov(X,Y).
(Hint: For the covariance, consider Var(X+Y))
X
1
2
3
4
5
P(X)
0.2
0.3
0.1
0.3

(1-x)y'' + xy' - y = 2(x-1)^2 e^(-x), 0 < x < 1
Find the general solution of the ODE

d^2/dx^2*y(x) +64y(x) = 0, select all solutions.
a) y(x) = C1sin(9x)
b) y(x) =9cos(8x)
c) y(x) = C2cos(2x)
d) y(x) = 9sin(9x) + 5cos(9x)
e) y(x) = 9cos(2x)

Let the random variable X and Y have the joint pmf f(x, y) =
xy^2/c where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} .
(a) Find c > 0 .
(b) Find μX
(c) Find μY
(d) Find σ^2 X
(e) Find σ^2 Y
(f) Find Cov (X, Y )
(g) Find ρ , Corr (X, Y )
(h) Are X...

Consider the joint pdf
f(x, y) = 3(x^2+ y)/11
for 0 ≤ x ≤ 2, 0 ≤ y ≤ 1.
(a) Calculate E(X), E(Y ),
E(X^2), E(Y^2), E(XY
), Var(X), Var(Y ),
Cov(X, Y ).
(b) Find the best linear predictor of Y given
X.
(c) Plot the CEF and BLP as a function of X.

Determine the type of below equations and solve it.
a-)(sin(xy)+xycos(xy)+2x)dx+(x2cos(xy)+2y)dy=0
b-)(t-a)(t-b)y’-(y-c)=0 a,b,c are
constant.

1. for 0<= x <=3 0<=x<=1 f(x,y) = k(x^2y+ xy^2)
a. Find K joint probablity density function.
b. Find marginal distribution respect to x
c. Find the marginal distribution respect to y
d. compute E(x) and E(y) e. compute E(xy)
f. Find the covariance and interpret the result.

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