Let X1 and X2 have a joint pdf
Let Find the joint pdf of Y1 and Y2.
Please do by hand. Thanks in advance. 5. Let X1 and X2 have joint pdf f(x1, x2) = 4xı, for 0 < x < x2 < l; and 0 otherwise. Find the pdf of Y = X/X2. (Hint: First find the joint pdf of Y and Y2 = X1.)
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
1. Let X1 and X2 have the joint pdf f(x1, x2) = 2e-11-22, 0 < 11 < 1 2 < 0o, zero elsewhere. Find the joint pdf of Yı = 2X1 and Y2 = X2 – Xı.
Let X = (X1, X2) be a 2 x 1 random vector having joint pdf (1 x € (0, 1) ~ [0, 1] 10 otherwise. Find the probability P(X1 < 0.5, X2 < 0.5)
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
3. Let (X1, X2) have the joint p.d.f 1 if 0 <1,0 < <1 f(1, ) else Find P(X1X2 < 0.5)
Let the random variables x and y have joint pdf as follows: 4 x < 1,0< y< 3 0 3 2) (round off to third decimal place). Find P(X>
X1 and X2 are IID with the density: a) joint density with r.v. Y1 = X1 and Y2 = X1 + X2 (I think this might be transformation but I'm stuck after) b) marginal density for Y2 f(x) = V2nz exp (-2) , for x>0,
The joint density of random variables X1, X2 is given by fx1,x2 (x1, 2)= 6x1, for 0 < xı < 1, 0 2 <1 - r Let Y X1X2. Find the joint density of Yi and Y2 Х1, Y?