Question

the answer should be 4/3 x

u Lipulation of X given Y =y? 10. Let X and Y have joint density (2xy for 0 Sy < 2x < 2 f(x, y) = { otherwise. What is the conditional expectation of Y given X = r?

Answer 1

TOPIC:Conditional expectation.

10.) The joint bol of x and Y is given as - Hex, y) = { 2xy ; o 24 3 2 x 52. o ; elew here . So, the marginal bdf of x is- - dx (x) = f dex,y) dy, 22 exy dy = 2x. [22 = 2x. (2x)² = |dx (x) = 54x² ; don, O EXE1. ".0 £2x 22 elewhere 1 = 0 en El. The conditional bef of (y1x=2) is - (2,7) - dylx= x (a) = de (X) 2xy . 4x3 2x²

so, deze (8) (8) OLJ £ 2x 044422 Y(XIX 2x2 o elew here. which is valid for ally o Lasl. - Now, we need, = € [y1x=2] 7.drikez Caj dy то 22 (C22)).