Question

Please answer all parts of the question. Thank you

[1] The joint probability density function of two continuous random variables X and Y is fx,x(x,y) = {6. sc, 0 Sy s 2.y = x < 4-y otherwise Find the value of c and the correlation of X and Y.

Answer 1

ANSWER Criven that Tuy osy<2, Yexsuy fxy(x,y) otherwise o find value of ci- we know that If the deady = u-y dady =1 2 (u-y-y) dy 2. 949-2be с C =4 (5) 2 Now find correlation of x 4 ay cm (X,5) = Coulxia) Cor (x,b) E (XY) - E(X) EU indly SI rung a laudy 2 . Solarze tray(0,5) din EX) = El)=2 similar find E) = ello EX) I dady

- 2. 2. 11 o Cov (x,y) = 4 (Car(x,y)=0 Correlation afx and y or(x,y) Cou(x,y) Hence 2 Var (x) Var (^)) Vailt) Van (y) Bence Correlation of x and , il 0