Question

Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer

Answer 1

My(t) E(etx) 920 e .1 Nuichis Momont generat ong ot+67 funetion ECex) Jl4 f 2coukSierx e to 01-U 2X 2. e wait itud intbib trion vler)Ele)E (e") e'r 2 TOO e(e-1)

(b) ECex) .1 1 #. -lS 17 w(e) 1. 1 1 . and y(x)e 1/ Ql0)= and y(o) = 1hure L=0 1 Rnow E Cex) - E(1+ X+Xl x3, 212 hoe - El1 +2 41 DECA) appeoxi mation is Yisodd only tape ist two term that is in our lake Ele)E(12) 1.5 60 more we 1-1 the twrms battar we ge fappoximab on So that is good but not good enouglh Sinilanly alalE)E'e) 1 + 2X t 4x2 - 21 72) wich is not =F 2 od enugh