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
X1 and X2 are IID with the density: a) joint density with r.v. Y1 = X1...
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?
Let X1 and X2 have a joint pdf Let Find the joint pdf of Y1 and Y2. f(x, y) = + y, 0<x,y<1
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.
5.4.([1] 5.6) The joint density function for Y1 and Y2 is f(y1,92) = {o 0 < y1 = 1,0 < y2 = 1 else a) what is P[Y1-Y2>0.5]? b) what is P[Y|Y2<0.5]?
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.
Let X1, X2, ..., Xn be iid random variables with a "Rayleigh” density having the following pdf: 22 -12 10 f(x) = e x > 0 > 0 0 пе a) (3 points) Find a sufficient estimator for 0 using the Factorization Theorem. b) (3 points) Find a method of moments estimator for 0. Small help: E(X1) = V c) (7 points) What is the MLE of 02 + 0 – 10 ? d) (7 points) For a fact, 21–1...
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.)
Let Xi and X2 be two continuous random variables having the joint probability density f,2)10 0, elsewhere. a. the joint pdf o1% and Y2.9(Y1,Y2), b, the P06 > Yi), c. the marginal pdfs gn () and g2(2), d. the conditional pdf h(walvi), and e. the E(Yalki-y) and E(gYi = 1/2).
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.
5.3.([1] 5.5) The joint density of Y and Y2 is given by 0 < y2 < y1 <1 else f(y1.92) = {3 a) Find F (33) = P[Y; <z, Y s. b) Find P[Y2 = ").