Please note that the
distributional form of Y was not given in the question and that is
why I wrote down the last portion in the square bracket.
have the prior pdf 2-2) Let a (e)-0<a<e where B>1 1 Find the joint pdf fo,...
Let (X,Y) have joint pdf given by f(rw)-y <x, 0 < x < 1, | 0, 0.W., (a) Find the constant c. (b) Find fx (x) and fy(y) (c) For 0 < x < 1, find fy|x=r(y) and My X=r and oỉ x=x (d) Find Cov(X,Y). (e) Are X and Y independent? Explain why.
Let X1 and X2 have a joint pdf
Let
Find the joint pdf of Y1 and Y2.
f(x, y) = + y, 0<x,y<1
Let X and Y have joint pdf f(x, y)= e if 0 < x < y< o and zero otherwise. Find Е(X |у). 16.
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
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 (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0, О.w., (a) Find the constant c (b) Find fx(x) and fy(y) (c) For 0 x< 1, find fyx=r (y) and py|x=x and oyx= (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...
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 X and Y have the joint pdf f(x,y) = e-x-y I(x > 0,y > 0). a. What are the marginal pdfs of X and Y ? Are X and Y independent? Why? b. Please calculate the cumulative distribution functions for X and Y, that is, find F(x) and F(y). c. Let Z = max(X,Y), please compute P(Z ≤ a) = P(max(X,Y) ≤ a) for a > 0. Then compute the pdf of Z.
Let the random variable X and Y have joint pdf f(x,y)=4/7(x2 +3y2), 0<x<1, 0<y<1 a. find E(X) and E(Y) b. find Var(X) and Var(Y) c. find Cov (X,Y)