Let X =( X1,
X2, X3 ) have the joint pdf
f(x1, x2,
x3)=60x1x22, where
x1...
Let X =( X1,
X2, X3 ) have the joint pdf
f(x1, x2,
x3)=60x1x22, where
x1 + x2 + x3=1 and
xi >0 for i = 1,2,3. find the
distribution of X1 ? Find
E(X1).
Find the matrix for each of the following quadratic forms.
(a)
q(x1,
x2, x3) =...
Find the matrix for each of the following quadratic forms.
(a)
q(x1,
x2, x3) =
7x12 +
3x22 −
4x32 +
12x1x2 +
18x2x3
b)
q(x1,
x2, x3) =
x1x2 +
x1x3 −
x2x3
I am having a general question for linear equation. Suppose we
have matrix A, B,x where...
I am having a general question for linear equation. Suppose we
have matrix A, B,x where A is non-invertible and A,B,x are 3x3
matrices. If we have Ax= B mod 26, then how do we solve for x?
Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) =...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b
< 1
then,
Show the density of the statistic T = X(n) is given by
FX(n) (x) = n/ab * (x/a)^{n/(b-1}} for 0 <= x <=
a ; otherwise zero.
# using the following
P (X(n) < x ) = P (X1 < x, X2 < x, ,,,,,,,,, Xn < x
),
Then assume...
Find the matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T...
Find the matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That
is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an
orthogonal matrix ?I any case,find the eigen values and eigen
vectors of A .
Suppose X1, X2, X3, and
X4 are independent and identically distributed random
variables with mean 10...
Suppose X1, X2, X3, and
X4 are independent and identically distributed random
variables with mean 10 and variance 16. in addition, Suppose that
Y1, Y2, Y3, Y4, and
Y5are independent and identically distributed random
variables with mean 15 and variance 25. Suppose further that
X1, X2, X3, and X4 and
Y1, Y2, Y3, Y4, and
Y5are independent. Find Cov[bar{X} + bar{Y} + 10,
2bar{X} - bar{Y}], where bar{X} is the sample mean of
X1, X2, X3, and X4 and
bar{Y}...