Question

Need step by step explanation with the formula used.  

Following is my question that has been answered:

I received the following answer to the questions. However, I do not understand what formula was used in part b and c. Could anyone help me to understand the solution with more details?

Thanks!

Specify each of the following. (a) The conditional distribution of X,, given that X2-X2 for the joint distribution with, μ1-0,P2-2, σ11-2, σ22-1, and P12:5 (b) The conditional distribution of X2, given that X1 - X1 and X3X3 for the joint distribution in Let X be N3 (H, 2) with ' [-3, 1, 4] and 1 -2 0 -2 5 0 L00 2 (c) The conditional distribution of X3, given that Xx and X2x2 for the joint distribution in Let X be N3 , Σ) with μ,-2,-3, 1] and 132 12 2 σ11 σ22 Var(Xi|Xp = x2) = (1-Pie)o11 = (3/4)82-1.5 "1 - 2 (c) E(XyX,-x1 , x2-x2) = 1 + ( 1.2) Var(XyXi = x1 , x2 = x2) = (1,2) =1/2+2/2 = 3/2=1.5 i 3) 2

Answer 1

Somt nơw.ad llistnibution Hh E (X.lx,): ss,+ 2,ふ(X2.u.) 22,6 2