. For the function x,y=xarctan(xy) , compute
fx , fy ,
fxx , fyy , and...
. For the function x,y=xarctan(xy) , compute
fx , fy ,
fxx , fyy , and
fxy
Compute the gradient of the function
fx,y,z=cos(xy+z)
Solution:
Find the divergence and the curl of the...
Compute the gradient of the function
fx,y,z=cos(xy+z)
Solution:
Find the divergence and the curl of the vector field
F=2z-xi+x+yj+(2y-x)k
1. Let (X; Y ) be a continuous random vector with joint
probability density function
fX;Y...
1. Let (X; Y ) be a continuous random vector with joint
probability density function
fX;Y (x, y) =
k(x + y^2) if 0 < x < 1 and 0 < y < 1
0 otherwise.
Find the following:
I: The expectation of XY , E(XY ).
J: The covariance of X and Y , Cov(X; Y ).
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the...
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...
The joint PDF of X and Y is given by
fX,Y(x, y) = nx^ne^(?xy) , 0...
The joint PDF of X and Y is given by
fX,Y(x, y) = nx^ne^(?xy) , 0 < x < 1, y > 0,
where n is an integer and n > 2.
(a) Find the marginal PDF of X and its mean.
(b) Find the conditional PDF of Y given X = x.
(c) Deduce the conditional mean and the conditional variance of
Y given X = x.
(d) Find the mean and variance of Y .
(e) Find the...
i)Please state if the following equations are exact or not:
(a) (sin(xy) − xy cos(xy))dx +...
i)Please state if the following equations are exact or not:
(a) (sin(xy) − xy cos(xy))dx + x^2 cos(xy)dy = 0
(b) (x^3 + xy^2 )dx + (x^2 y + y^3 )dy = 0
ii) Determine if the following equation is exact, and if it is
exact, find its complete integral in the form g(x, y) = C:
(3(x)^2 + 2(y)^2 )dx + (4xy + 6(y)^2 )dy = 0
Consider the random variables X and Y with the following joint
probability density function:
fX,Y (x,...
Consider the random variables X and Y with the following joint
probability density function:
fX,Y (x, y) = xe-xe-y, x > 0, y
> 0
(a) Suppose that U = X + Y and V = Y/X. Express X and Y in terms of
U and V .
(b) Find the joint PDF of U and V .
(c) Find and identify the marginal PDF of U
(d) Find the marginal PDF of V
(e) Are U and V independent?
Let fX,Y be the joint density function of the random variables X
and Y which is...
Let fX,Y be the joint density function of the random variables X
and Y which is equal to fX,Y (x, y) = { x + y if 0 < x, y <
1, 0 otherwise. } Compute the probability density function of X + Y
. Referring to the problem above, compute the marginal probability
density functions fX(x) and fY (y). Are the random variables X and
Y independent?
Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy -...
Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy - 3x - 5. Then determine whether each critical point is a local
maximum, local minimum, or saddle point. Then find the value of the
function at the extreme(s).