Piling-Up Principle Consider the discrete random variable, X i ④Ⅹ the probability distribution will be PrXx=0]=p1*p1+(1-p)*(1-P) PxX⊕x1=1]=p*(1-)+(1-p)(p bias of X;is:6;=p;-12;-1/2∈8;<=h; Prx;=0=佐+ rX;=1l=佐-8 for I=1, 2,..and 1 <12<13 ④..”a23 ik be the bias of the random variable X小 let￡ ④Ⅹ the en e 8.为 826 Piling-Up Principle Consider the discrete random variable, Xi  Xj ; the probability distribution will be: Pr[Xi  Xj = 0] = pi*pj + (1-pi )*(1-pj ); Pr[Xi  Xj = 1] = pi*(1-pj ) + (1-pi )*(pj ); bias of Xi is:  i = pi –1/2; -1/2 <= i <= ½; Pr[Xi = 0] = ½ +  i ; Pr[Xi = 1] = ½ -  i ; for I = 1,2,…… and i1 < i2 < i3……<ik ; let i 1 , i2 ,i3 ,….ik be the bias of the random variable Xi 1  …..  Xi k ; then  i 1 ,i2 , = 2  i 1 *  i 2