Find P(X^2 < Y < X) if X and Y are jointly distributed with pdf f(x, y) = 2x; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.
Find P(X^2 < Y < X) if X and Y are jointly distributed with pdf f(x,...
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
Suppose X and Y are jointly distributed with density \ a. Find c. (b) Find the marginal distribution of X and Y. (c) Find P(X > 2). (d) Find (E[X2 ]). (e) Find the conditional distribution of Y, given that X = 1. (f) E[X], E[Y], E[XY], Cov(X,Y) and ρXY f(x,y)ce-(=/2+y/4) 0<y<I < 0 otherwise 0 f(x,y)ce-(=/2+y/4) 0
.1. Two discrete random variables X and Y are jointly distributed. The joint pmf is f(z, y) = 1/28 , SX = {0, 1, 2, 3, 4, 5,6}, and SY = {0, .... X), where Y is a non-negative integer a) Find the marginal pdfs of X and Y b) Caculate E(X) and E(Y). 2. Let the joint pdf of X aud Y be a) Draw the graph of the support of X and Y b) Determine c in the joint pdf. c) Find E(X +Y),...
X and Y are jointly continuous with joint pdf fa,y) - Otherwise Find c. b. Find P(X Y <1). c. | Find marginal pdrs of X and of Y. . Are X and Y independent? Justify. 2 pt. 2 p 2 pt. 2 pt. /cof, sto , 24
9. Suppose that the jointly distributed random variables X and Y have the following pdf (a) Find E(X +Y). (b) Find Cov(X, Y)
The joint pdf of X and Y is f(x, y) = x for x > 0, y > 0, x + y < 2. (a) Find P(Y > 2X). (b) Find E(XY). (c) Find P(0.7 < X < 1.71Y = 0.5).
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.
Problem 7: Let X and Y be two jointly continuous random variables with joint PDF 4 (x y) otherwise a) Find P(0< Y< 1/2 I x-2) b) For what value of A is it true that P(0 < Y < ½ |X> A)-5/16