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...
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T :...
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?
Suppose that X and Y have the following
joint probability density function.
f (x, y) = ...
Suppose that X and Y have the following
joint probability density function.
f (x, y) =
3
332
y, 0 < x < 5, y
> 0, x − 4 < y < x +
4
(a)
Find E(XY).
(b)
Find the covariance between X and Y.
the random variable x and y have joint density function given by
fx,y={ A(1+x). , 0<=x<=1;0<=y<=3...
the random variable x and y have joint density function given by
fx,y={ A(1+x). , 0<=x<=1;0<=y<=3 0 elsewhere 3.1
determine the value of constant A for proper p.d.f ?3.2 find the
expected values of X and Y?3.3. obtain the covariance of X and
Y?3.4 determine if x and y are statistically independent.
15.1The probability density function of the X
and Y compound random variables is given below.
X  
15.1The probability density function of the X
and Y compound random variables is given below.
X
Y
1
2
3
1
234
225
84
2
180
453
161
3
39
192
157
Accordingly, after finding the possibilities for each value, the
expected value, variance and standard deviation; Interpret the
asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005)
according to the arithmetic mean and the kurtosis measure
(a4) when the 4th moment (µ4 = 0.004) according to the
arithmetic...