Suppose f(x,y)=c(2x+3y) for 0<x<1 and 0<y<1
Find c.
Find F(x,y).
Use your answer from part b....
Suppose f(x,y)=c(2x+3y) for 0<x<1 and 0<y<1
Find c.
Find F(x,y).
Use your answer from part b. to find p(X<0.5,
Y<0.5).
f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the...
f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the gradient of f.
∇f(x, y, z) =
< , , >
(b) Evaluate the gradient at the point P.
∇f(1, 0, 3) = < , ,
>
(c) Find the rate of change of f at P in the
direction of the vector u.
Duf(1, 0, 3) =
Consider
f(x, y) = (x ^2)y + 3xy − x(y^2)
and point P (1, 0).
Find...
Consider
f(x, y) = (x ^2)y + 3xy − x(y^2)
and point P (1, 0).
Find the directional derivative of f at P in the direction of ⃗v
= 〈1, 1〉. Starting from P , in what direction does f have the
maximal rate of change? Calculate the maximal rate of change
Find the hyperbolic equation
8) Foci F(±4, 0) and asymptotes y = ± [x√(14) / √(2)]...
Find the hyperbolic equation
8) Foci F(±4, 0) and asymptotes y = ± [x√(14) / √(2)]
9) Foci F(0, ±√(19)) and asymptotes y = ± [2x√(3) / √(7)]
10) Foci F(±11, 0) and asymptotes y = ± [2x√(10) / 9]
Consider the following joint distribution between random
variables X and Y:
Y=0
Y=1
Y=2
X=0
P(X=0,...
Consider the following joint distribution between random
variables X and Y:
Y=0
Y=1
Y=2
X=0
P(X=0, Y=0) = 5/20
P(X=0, Y=1) =3/20
P(X=0, Y=2) = 1/20
X=1
P(X=1, Y=0) = 3/20
P(X=1, Y=1) = 4/20
P(X=1, Y=2) = 4/20
Further, E[X] = 0.55, E[Y] = 0.85, Var[X] = 0.2475 and Var[Y] =
0.6275.
a. (6 points) Find the covariance between X and Y.
b. (6 points) Find E[X | Y = 0].
c. (6 points) Are X and Y independent?...
Let f(x, y) = 1/2 , y < x < 2, 0 ≤ y ≤ 2...
Let f(x, y) = 1/2 , y < x < 2, 0 ≤ y ≤ 2 , be the joint
pdf of X and Y .
(a) Find P(0 ≤ X ≤ 1/3) .
(b) Find E(X) .
(c) Find E(X|Y = 1) .