Piling-Up Principle Suppose that X, X2, X3. are independent random variables taking the values from set 10, 1) Let pl, p2, p3. Be real number such that O<=p; <=1 Pr[x1=0]=p; (1=1,2,3,4…. Pr[X1=1]=1p1 Suppose il=j the independence implies that PX1=0,X=0]=pp rx=0,×1;=1=p(1-p1) PX=1,x1=0]=(1p1) P[X=1,x=1]=(1p1)*(1p1)25 Piling-Up Principle Suppose that X1 , X2 , X3… are independent random variables taking the values from set {0, 1}. Let p1 , p2 , p3…. Be real number such that 0<= pi <=1 ; Pr[Xi = 0] = pi ; (i = 1, 2, 3, 4 ……..) Pr[Xi = 1] = 1-pi ; (i = 1, 2, 3, 4 ……..) Suppose i != j: the independence implies that:- Pr[Xi = 0, Xj = 0] = pi*pj ; Pr[Xi = 0, Xj = 1] = pi*(1-pj ); Pr[Xi = 1, Xj = 0] = (1-pi )*pj ; Pr[Xi = 1, Xj = 1] = (1-pi )*(1-pj );