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 X1 and X2 have a joint pdf Let Find the joint pdf of Y1 and Y2. f(x, y) = + y, 0<x,y<1
2. (10 marks) Let X, and X, be two random variables with joint pdf 3.1 0 < x <3 <1; xix,( 22) - Yo elsewhere. a) Are X, and X, independent? If not, find E(X,X2). b) Are X, and X, correlated? Find Cou(X1, X2).
0 2.2.8. Suppose X1 and X2 have the joint pdf I e-le-22 21 > 0, X2 > 0 f(x1, x2) = elsewhere. For constants w1 > 0 and W2 > 0, let W = W1X1 + W2X2. (a) Show that the pdf of W is 1 -(e-w/wi – e-W/W2) W > 0 fw(W) = { W1-W2 C 10 elsewhere. (b) Verify that fw(w) > 0 for w > 0. (c) Note that the pdf fw(w) has an indeterminate form when...
Let X1 and X2 have joint PDF f(x1,x2)=x1+x2 for 0 <x1 <1 and 0<x2 <1.(a) Find the covariance and correlation of X1 and X2. (b) Find the conditional mean and conditional variance of X1 given X2 = x2.
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.
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?
2.1.1. Let f(x1,x2) = 4x1x2 , 0 < 띠 < 1, 0 < x2 < 1, zero elsewhere, be the pdf of Xi and X2. Find P(0 < Xìく, ¼ < X2 < 1), P(Xi = X2), P(Xi < X2), and Hint: Recall that P(X1 -X2) would be the volume under the surface f(xi, r2)- 4 t 0 < x1 = x2 < 1 in the x1x2-plane. T102 and above the ne segmen
3. Let (X1, X2) have the joint p.d.f 1 if 0 <1,0 < <1 f(1, ) else Find P(X1X2 < 0.5)
2. Let X1 and X2 have the joint pmf p(11, 12) = 232, 21 = 1,2,3 and x2 = 1,2,3, zero elsewhere. Find the joint pmf of Y1 = X1 X2 and Y2 = X2, and then find the marginal pmf of Y.