The random variables X and Y have the joint PDF fx,y(x,y)=0.5, if x>0 and y>0 and...
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?
Let X and Y be continuous random variables with following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.
Let X and Y be a random variable with joint PDF: f X Y ( x , y ) = { a y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise What is a? What is the conditional PDF of given ? What is the conditional expectation of given ? What is the expected value of ? Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
The random variables X and Y have joint PDF fX,Y(x,y) = {12x2y 0<=x<=c; 0 <= y <= 3 { 0 otherwise (a) FInd the value of C (b) Find the PDF fW(w) where W = X / Y (c) Find the PDF fZ(z) where Z = min(X,Y)
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
Let X and Y be continuous random variables with joint pdf fx,r (x, y)-3x, 0Sysx3s1, and zero otherwise. 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?
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. 、
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y |X = x. (d) Find P(Y < 3|X = 1). Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
X and Y are random variables with the joint PDF fx.^(t,y)-65536 0 otherwise. (a) What is the marginal PDFfx(x)? ㄑㄨ 8 5xA4/65536 fx(x) 0 otherwise (b) What is the marginal PDF fy(v)? (5 * 843)/(3*655 0 〈y〈 64 fy(y) = 0 otherwise