The joint PDF of two continuous random variables X and y is given: S(x, v) = e,x> 0, y> 0. Let U = XY and V Use transformation Y technique to determine the joint PDF of g(u, v)
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- Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of YLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.
- The joint PDF of two continuous random variables X and y is given: S(x, y) = e**), x> 0, y > 0. Let U = XY and V : Use transformation Y %3D technique to determine the joint PDF of g(u, v)Let X and Y be continuous random variables having a joint pdf given by f(x, y) = e-*, 0sysx 3).Suppose Y1 and Y2 are random variables with joint pdf (6(1 — у2), 0, 0 < y1 < y2 fv, otherwise Y1 Let U1 and U2 = Y,. Use the transformation technique to show that U, follows a uniform Y2 distribution from 0 to 1.
- Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?
- Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{OWe have a random variable X and Y that have the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what would the pdf of the random variable U be? What is the support for the random variable U? Would there be any critical points? (use CDF technique)Assume that X and Y are independent random variables where X has a pdf given by fx(x) = 2aI(0,1)(x) and Y has a pdf given by fy(y) = 2(1– y)I(0,1)(y). Find the distribution of X + Y.SEE MORE QUESTIONS