![Q4. Suppose X is a random variables with possible values -1,1 and Y is another with possible values -1, 0,1. Suppose the joint probability distribution of X, Y, f(x, y), is given by: a. Find the marginal distribution of X and Y. b. Find E[Xly1] c. Compute Cov(X, Y) d. Are X, Y independent? justify e. Compute E(XYorl](http://img.homeworklib.com/questions/5ec4c050-74ea-11ea-b09c-6fae502e6371.png?x-oss-process=image/resize,w_560)
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Q4. Suppose X is a random variables with possible values -1,1 and Y is another with...
1. Suppose you have two random variables, X and Y with joint distribution given by the...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
A step by step solution 2. Suppose X and Y are random variables with joint probability...
A step by step solution
2. Suppose X and Y are random variables with joint probability density function of the form f(x, y) +y, for 0 S r S 1; and 0 SyS 1 and zero elsewhere. (a) Find the marginal distribution of X and Y. (b) Compute E(X), E(Y); Var(X) and Var(Y). (c) Compute Cov(X, Y). (d) Compute El(2X - Y)
The discrete random variables X and Y take integer values with joint probability distribution given by...
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit...
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit square [0, 1] x [0, 1]. (a) Let F(r,y) be the joint CDF. Compute F(1/2, 1/2). Compute F(z,y). (b) Compute the marginal densities for X and Y (c) Are X and Y independent? (d) Compute E(X), E(Y), Cov(X,y)
Q3. . Suppose that joint probability function of X and Y is given by | 1/7,...
Q3. . Suppose that joint probability function of X and Y is given by | 1/7, z = 5, y = 0 Px,y(, ) 0, otherwise. a. Find the marginal distribution of X and Y b. Find E(X|y = 4] c. Compute Cov(X, Y). d. Are X, Y independent? justify e. Compute E[XY0or4] f. Find px(8) and P(Y-4X-8).
Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 <...
Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 < y < x < 1. a) Find constant c that makes f (x, y) a valid joint pdf. b) Find the marginal pdf of X and the marginal pdf of Y. Remember to provide the supports c) Are X and Y independent? Justify
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...
you have two random variables, X and Y with joint distribution given by the following table:...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
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.
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
A step by step solution
2. Suppose X and Y are random variables with joint probability density function of the form f(x, y) +y, for 0 S r S 1; and 0 SyS 1 and zero elsewhere. (a) Find the marginal distribution of X and Y. (b) Compute E(X), E(Y); Var(X) and Var(Y). (c) Compute Cov(X, Y). (d) Compute El(2X - Y)
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit square [0, 1] x [0, 1]. (a) Let F(r,y) be the joint CDF. Compute F(1/2, 1/2). Compute F(z,y). (b) Compute the marginal densities for X and Y (c) Are X and Y independent? (d) Compute E(X), E(Y), Cov(X,y)
Q3. . Suppose that joint probability function of X and Y is given by | 1/7, z = 5, y = 0 Px,y(, ) 0, otherwise. a. Find the marginal distribution of X and Y b. Find E(X|y = 4] c. Compute Cov(X, Y). d. Are X, Y independent? justify e. Compute E[XY0or4] f. Find px(8) and P(Y-4X-8).
Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 < y < x < 1. a) Find constant c that makes f (x, y) a valid joint pdf. b) Find the marginal pdf of X and the marginal pdf of Y. Remember to provide the supports c) Are X and Y independent? Justify
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...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) 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.
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