1 Let Zi Z2 Z3N01 independent CalculateVar Calculate Var Cal

1. Let Zi, Z2, Z3N(0,1) independent CalculateVar Calculate Var Calculate P(max(Z1, Z2)>)

Solution

2) E(x) = np

var(x) = np(1-p)

a) x1= z1+2z2

= var(x) = 1*(1/2)^2 + 2*1*(1/2)^2 = 1/4 + 1/2 = 3/4

e(x) = 1*(1/2) + 2(1/2) = 3/2

b) x2= -z2+2z3

var(x) = -1*(1/2)^2+ 2*(1/2)^2 = -1/4+1/2 = 1/2

e(x) = -1(1/2) + 2*(1/2) = 1/2