Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
(1 point) Let f(x Scxºy? if 0 < x < 1, 0 SY51 otherwise Find the following: (a) c such that f(x,y) is a probability density function: c= (b) Expected values of X and Y: E(X) = E(Y) = 100 (c) Are X and Y independent? (enter YES or NO)
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
HW on independent rivins I - © Let sa o<x<1 - ocy<x</ f(x,y)= z ó otherwise and the correlation Find Coo (X,Y) coefficient s. X ② Let 8(x, y) -f / 1 e 2 xso, y so otherwise and the correlation Find Coo (X,Y) coefficient s.
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
4. (30 pts) Let (X,Y) have joint pdf given by e-y, 0 < x < y < 0, f(x,y) = { | 0, 0.w., (a) Find the correlation coefficient px,y. (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
4. (30 pts) Let (X,Y) have joint pdf given by < , | e-9, 0 < x < f(x,y) = 3 | 0, 0.w., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Let f(x, y) = kxy, for 0 <x< 1 and 0 <y<1 and 0 elsewhere, a) Find k b) Find marginal pdfs. c) Are X and Y independent? d) Find P(X<0.5, Y>0.5).