Question

(d) E(Y|X) and Var(Y|X).

Answer #1

Consider two random variables X and Y such that E(X)=E(Y)=120,
Var(X)=14, Var(Y)=11, Cov(X,Y)=0.
Compute an upper bound to
P(|X−Y|>16)

1) Suppose that X and Y are two random variables, which may be
dependent and Var(X)=Var(Y). Assume that 0<Var(X+Y)<∞ and
0<Var(X-Y)<∞. Which of the following statements are NOT true?
(There may be more than one correct answer)
a. E(XY) = E(X)E(Y)
b. E(X/Y) = E(X)/E(Y)
c. (X+Y) and (X-Y) are correlated
d. (X+Y) and (X-Y) are not correlated.
2) S.D(X ± Y) is equal to, where S.D means standard
deviation
a. S.D(X) ± S.D(Y)
b. Var(X) ± Var(Y)
c. Square...

Suppose X and Y are independent variables with E(X) = E(Y ) = θ,
Var(X) = 2 and Var(Y ) = 4. The two estimators for θ, W1 = 1/2 X +
1/2 Y and W2 = 3/4 X + 1/4 Y .
(1) Are W1 and W2 unbiased? (2) Which estimator is more
efficient (smaller variance)?

E[X] = 2, E[X^2] = 8, E[Y] = 8, E[Y^2] = 100, and Var(X +Y) =
60. What is ρ(X, Y ), the correlation of X and Y

If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) =
1, Var(Y) =2, ρX,Y = −0.5
(a) For Z = 3X − 1 find µZ, σZ.
(b) For T = 2X + Y find µT , σT
(c) U = X^3 find approximate values of µU , σU

If X and Y are independent, then var(XY) = var(X)*var(Y),is that
right? why?

Let X and Y denote be as follows: E(X) = 10, E(X2) =
125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155. Let W = 2X-Y and
let T = 4Y-3X. Find the covariance of W and T.

If E(X)=1 and Var(X)=5, find Var( 2X+5)

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.

given x,y are independent random variable. i.e
PxY(X,Y)=PX(X).PY(Y). Prove
that
(1)
E(XK.YL)=E(XK).E(YL).
Where K,L are integer(1,2,3-----)
(2) Var(x.y)= var(x).var(y).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 14 minutes ago

asked 23 minutes ago

asked 29 minutes ago

asked 31 minutes ago

asked 35 minutes ago

asked 52 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago