16) X & Y have joint pdf f(x, y) = 3xy, 0 < x <1, x < y < 2 − x Determine the marginal pdf of X on the interval (0, 1)
the answer is 6x – 6x^2
19) Suppose X & Y have a uniform (flat) pdf on the support of problem (16). Determine P(Y > 2X).
the answer is 2/3
I would like to know the answer of question 20 and question 21
20) Continuing problem (19), determine Var(Y | X = .75) a) 1/4 b) 1/12 c) 1/16 d) 1/24 e) 1/48
21) Continuing problem (19), determine Var(Y | X ≤ .75)
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
6. Suppose X and Y have the joint pdf fr,y) = 2 exp(-:- 0 ) 0< <y otherwise o a. Find Px.x, the correlation coefficient between X and Y. b. Let U = 2X-1 and V=Y +2. What is pu.v, the correlation coefficient between U and V? c. Repeat (b) if U = -TX and V = Y + In 2. d. Let W = Y - X. Compute Var (W). e. Refer to (d). Find an interval that will...
The joint pdf of X and Y is given by f(x, y) = C,0<x<y<1. a) Determine the value of C. b) Determine the marginal distribution of X and compute E(X) and Var(X). c) Determine the marginal distribution of Y and compute E(Y) and Var(Y). d) Compute the correlation coefficient between X and Y.
Suppose X, Y and Z are random variables with joint pdf f(x,y,z) = cxy2z if 0 < x ≤ 2, 0 ≤ y < 1, 0 < z < 1 0 otherwise a.) Find the constant c b.) Calculate P(1 < X ≤ 2, 0.5 ≤ Y < 1) c.) Calculate E(2X+2020) d.) Calculate Var(2X+2020) e.) Calculate E(XZ+2020) I think I understand how to do parts a and c, but I'm less certain of how to proceed on the rest...
Show all work! Thank you! 0<x<2, 0<y<1 23. The joint pdf of X and Y is fx.y(x, y)= (region below). 3 0 otherwise a) Determine f(y) b) Determine fx, (x) c) Determine E[Yx] d) Determine E[X|y] 0 1 2 24. Suppose that the joint probability density function of the jointly continuous random variables X and Y is x on the given region fxy(x,y)= 11 10 otherwise Determine fyly) 1 _$6x 0<x< y1 25. Let X and Y be continuous random...
Let X and Y have joint pdf f(x, y)= e if 0 < x < y< o and zero otherwise. Find Е(X |у). 16.
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)
7. Suppose X and Y have joint pdf f(x,y) = 24x y if x >0, y>0,x+y<1 and 0 otherwise. Find P(Y > 2x).
Suppose X, Y are random variables whose joint PDF is given by . 1 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).
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)