Question

Let X and Y denote the values of two stocks at the end of a 5 year-period. X is uniformly distributed on the interval (0, 10). Given X=x, Y is uniformly distributed on the interval (0, 2x).

Determine Cov[X, Y] according to this model.

Answer #1

Let X and Y denote the values of two stocks at the end of a 5
year-period. X is uniformly distributed on the interval (0, 10).
Given X=x, Y is uniformly distributed on the interval (0, 2x).
Determine Cov[X, Y] according to this model.

Let X and Y denote the values of two stocks at the end of a five
year period. X is uniformly distributed on the interval (0,12).
Given X=x, Y is uniformly distributed on the interval (0,x).
Determine Cov(X,Y) according to the model.

Let X denote the size of a bodily injury claim and Y denote the
size of the corresponding property damage claim. Let Z1 = X + Y.
From prior experience we know Var(X) = 144, Var(Y) = 64 and Var(X +
Y) = 308. It is expected that bodily injury claims will rise 10%
next year and property damage will rise by a fixed amount of 5. Let
Z2 be the new trial of bodily injury and property damage. Compute...

Two genes’ expression values follow a bivariate normal
distribution. Let X and Y denote their expression values
respectively. Also assume that X has mean 9 and variance 3; Y has
mean 10 and variance 5; and the covariance between X and Y is
2.
In a trial, 50 independent measurements of the expression values of
the two genes are collected, and denoted as 11 ( , ) XY, …, 50 50 (
, ) XY. We wish to find the...

Two genes’ expression values follow a bivariate normal
distribution. Let X and Y denote their expression values
respectively. Also assume that X has mean 9 and variance 3; Y has
mean 10 and variance 5; and the covariance between X and Y is 2. In
a trial, 50 independent measurements of the expression values of
the two genes are collected, and denoted as 1 1 ( , ) X Y , …, 50
50 ( , ) X Y ....

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.

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.

Let X denote the diameter of an armored electric cable and Y
denote the diameter of the ceramic mold that makes the cable. Both
X and Y are scaled so that they range between 0 and 2. Suppose that
X and Y have the joint density
f(x,y)={Ky00<x<y<2;otherwise.
Determine the value of the constant K.
Determine the FX,Y(0.5,1).

] Let X denote the size of a surgical claim and let Y denote the
size of the associated hospital claim. An analyst is using a model
in which Var[X] = 2.4, E[Y ] = 7, E[Y^2 ] = 51.4 and Var[X + Y ] =
8. If a 20% increase is added to the hospital portion of the claim,
find the variance of the new total combined claim

Let X denote the size of a surgical claim and let Y denote the
size of the associated hospital claim. An analyst is using a model
in which Var[X] = 2.4, E[Y ] = 7, E[Y^2]=51.4 and Var[X+Y]=8. If a
20% increase is added to the hospital portion oft he claim, find
the variance of the new total combined claim.

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