Please explain step by step, especially option b.
Please explain step by step, especially option b. 1. Continuous random variables X and Y have...
The random variables X and Y have the joint PDF -fa.. 2 0 S x s 1 0 Sy s1 (2х + Зу) fxy(x, y) = otherwise The mean squared error is defined as ET(X + Y - t)21, what value of t minimizes this error? The random variables X and Y have the joint PDF -fa.. 2 0 S x s 1 0 Sy s1 (2х + Зу) fxy(x, y) = otherwise The mean squared error is defined as...
The random variables X and Y have the joint PDF -fa.. 2 0 S x s 1 0 Sy s1 (2х + Зу) fxy(x, y) = otherwise The mean squared error is defined as ET(X + Y - t)21, what value of t minimizes this error? The random variables X and Y have the joint PDF -fa.. 2 0 S x s 1 0 Sy s1 (2х + Зу) fxy(x, y) = otherwise The mean squared error is defined as...
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)
Suppose X, Y are random variables whose joint PDF is given by fxy(x, y) 9 { 0 <y <1,0 < x <y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
Question 3 [17 marks] The random variables X and Y are continuous, with joint pdf 0 y otherwise ce fxx (,y) a) Show that cye fr (y) otherwise and hence that c = 1. What is this pdf called? (b) Compute E (Y) and var Y; (c) Show that { > 0 fx (a) e otherwise (d) Are X and Y independent? Give reasons; (e) Show that 1 E(XIY 2 and hence show that E (XY) =. Question 3 [17...
2. Let the random variables X and Y have the joint PDF given below: 2e -y 0 xyo0 fxy (x, y) otherwise 0 (a) Find P(X Y < 2) (b) Find the marginal PDFs of X and Y (c) Find the conditional PDF of Y X x (d) Find P(Y< 3|X = 1)
Show all work! Thank you! Sk(x+y) 0<x<1, 0<y</ 14. Determine k, so that fx.y(x, y)= otherwise is a joint pdf. 10 15. Determine k, so that fxy(x,y)= kry 0<x<1, 0<y<1. 6 otherwise is a joint pdf. k(xy?) 0<x<1, 0<y<1. is a joint pdf. Determine k, so that fx.x(x,y)= 1 otherwise 17. Determine k, so that fx.y(x,y)= kr 0<x<y<1 O otherwise is a joint pdf. k(x + y) 0<x< y<1 18. Determine k, so that fx. (x,y)= 1 0 otherwise is...
Section 6.5: Mean Square Estimation 6.68. Let X and Y be discrete random variables with three possible joint pmf's: Let X and Y have joint pdf: fx.y(x, y) -k(x + y) for 0 sxs 1,0s ys1 Find the minimum mean square error linear estimator for Y given X. Find the minimum mean square error estimator for Y given X. Find the MAP and ML estimators for Y given X. Compare the mean square error of the estimators in parts a,...
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).