The joint density function of continuous variables X and Y is (8 points) fry (x, y)...
The joint density function of continuous variables X and Y is (8 points) fry (x, y) = x y ; 0 < x < 1, 1 < y < 5 and= 0 elsewhere. i. Find the marginal density functions for X and Y, fx (x), fy (y). ii. Are X and Y independent?. Justify your answer.
Homework Answers
Add Answer to:
The joint density function of continuous variables X and Y is (8
points) fry (x, y)...
8. Suppose X and Y are jointly continuous with joint probability density function fx,Y(x, y) =...
8. Suppose X and Y are jointly continuous with joint probability density function fx,Y(x, y) = ce 2,JER, for some constant c (i) Find the value of constant c. (ii) Find the marginal density functions of X and Y (ii) Determine whether X and Y are independent.
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y)...
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
Suppose X and Y are continuous random variables with joint density function 1 + xy 9...
Suppose X and Y are continuous random variables with joint density function 1 + xy 9 fx,y(2, y) = 4 [2] < 1, [y] < 1 otherwise 0, (1) (4 pts) Find the marginal density function for X and Y separately. (2) (2 pts) Are X and Y independent? Verify your answer. (3) (9 pts) Are X2 and Y2 independent? Verify your answer.
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x...
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function...
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function of Y is given by 3es if y 0, 0 otherwise. fy (y) = (b) |3 poin s apute the marginal density function of X (c) [3 points] Show that E(X)Y = y) =-y-1, for y 0 (d) 13 points] Compute E(X) using the...
The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for...
The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for 0<X<1 and 0<Y<1. a) Find the expected value of X+Y. (b) Find fX(x), and fY(y). (c) Find Cov(X,Y). (d) Find Corr(X,Y).
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density f...
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
The continuous random variables, X and Y , have the following joint probability density function: ...
The continuous random variables, X and Y , have the following joint probability density function: f(x,y) = 1/6(y2 + x3), −1 ≤ x ≤ 1, −2 ≤ y ≤ 1, and zero otherwise. (a) Find the marginal distributions of X and Y. (b) Find the marginal means and variances. (c) Find the correlation of X and Y. (d) Are the two variables independent? Justify.
(II) Multiple continuous random variables: 8.2 Let X and Y have joint density fXY(x,y) = cx^2y...
(II) Multiple continuous random variables: 8.2 Let X and Y have joint density fXY(x,y) = cx^2y for x and y in the triangle defined by 0 < x < 1, 0 < y < 1, 0 < x + y < 1 and fXY(x,y) = 0 elsewhere. a. What is c? b. What are the marginals fX(x) and fY(y)? c. What are E[X], E[Y], Var[X] and Var[Y]? d. What is E[XY]? Are X and Y independent?
The joint probability density function for continuous random variables X and Y is given below. f...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
8. Suppose X and Y are jointly continuous with joint probability density function fx,Y(x, y) = ce 2,JER, for some constant c (i) Find the value of constant c. (ii) Find the marginal density functions of X and Y (ii) Determine whether X and Y are independent.
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
Suppose X and Y are continuous random variables with joint density function 1 + xy 9 fx,y(2, y) = 4 [2] < 1, [y] < 1 otherwise 0, (1) (4 pts) Find the marginal density function for X and Y separately. (2) (2 pts) Are X and Y independent? Verify your answer. (3) (9 pts) Are X2 and Y2 independent? Verify your answer.
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function of Y is given by 3es if y 0, 0 otherwise. fy (y) = (b) |3 poin s apute the marginal density function of X (c) [3 points] Show that E(X)Y = y) =-y-1, for y 0 (d) 13 points] Compute E(X) using the...
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
Most questions answered within 3 hours.
-
Preparation of Benzoic Acid using a Grignard Reagent URGENT
1. During your Grignard formation, a small...
asked 14 minutes ago -
A uniform magnetic field is perpendicular to the plane of a wire
loop. If the loop...
asked 13 minutes ago -
At the peak of your career, your were earning $120,000 and
holding a top level position....
asked 16 minutes ago -
. A permanent magnet is dropped south-end-down through a horizontal
circular coil with a radius of...
asked 18 minutes ago -
Bernie's Beverages purchased some fixed assets classified as
5-year property for MACRS. The assets cost $28,000....
asked 32 minutes ago -
How many ATPs are produced from the catabolism of a 10-C
molecule of fatty acid under...
asked 36 minutes ago -
Before practicing a routine on the rings, a 64.8 kg gymnast
hangs motionless, with one hand...
asked 38 minutes ago -
If the K b of a weak base is 6.3 × 10 − 6 , what...
asked 45 minutes ago -
Which of the following is the minimum amount of moles of NaOH
that must be added...
asked 48 minutes ago -
Stories about organizational ________ provide important clues
about cultural values and norms.
a. myths
b. heroes...
asked 50 minutes ago -
Explain the criteria used in selecting a target market
BUS220 Retail Management, thank you!
asked 52 minutes ago -
Convert/Calculate the following:
Determine the identity of an elemental gas if 4.55 L weighing
35.4g, under...
asked 55 minutes ago