Let fX,Y (x,y) = 24xy for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and 0 otherwise.
find the marginal pdf
find P(X<Y)
Let X and Y have the joint pdf fXY(x,y) = 24xy^3, 0<y<x<1. Find P(X>2/3, Y<1/3) Find P(X<2Y)
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
Let X and Y be continuous random variables with joint pdf fx y (x, y)-3x, 0 Sy and zero otherwise. 2. sx, a. What is the marginal pdf of X? b. What is the marginal pdf of Y? c. What is the expectation of X alone? d. What is the covariance of X and Y? e. What is the correlation of X and Y?
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]...
1. Consider a pair of random variables (X, Y) with joint PDF fx,y(x, y) 0, otherwise. (a) 1 pt - Find the marginal PDF of X and the marginal PDF of Y. (b) 0.5 pt - Are X and Y independent? Why? (e) 0.5 pt - Compute the mean of X and the mean of Y.
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
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)
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).