independent X1,X2,,Xn∈{0，l} X=∑X EX= 2=1 Pr[X≥(1+δ) for入>0 eeng whenλ=ln(1+) =
X = X n i=1 Xi E[X] = µ independent X1, X2,...,Xn 2 {0, 1} Pr[X (1 + )µ] X (1+)µ Pr e e for > 0 ∑ √ e(e∏°1) e∏(1+±) !µ when ⇥ = ln(1+) e (1+) = (1+) µ
independent X1,X2,...,XnE {0,1) X=Xi EX= 2=1 Pr[X≥(1+0)w forλ>0 Pre4x≥ea1+op叫s ): ex(1+5) =eie=env-e i=1 p=Pr[X=1=∑ Pi i=1 whenλ=ln(1+)
X = X n i=1 Xi E[X] = µ independent X1, X2,...,Xn 2 {0, 1} Pr[X (1 + )µ] X (1+)µ Pr e e E e⇥X ⇥ e⇥(1+)µ for > 0 pi = Pr[Xi = 1] µ = X n i=1 pi n i=1 epi(e1) e(e1)µ = ∑ √ e(e∏°1) e∏(1+±) !µ ∑ √ e± (1+±)(1+±) !µ when ⇥ = ln(1+) = n i=1 E ⇥ eXi ⇤ = E ⇤ n i=1 eXi ⇥
Chernoff Bound independent X1,X2,..,Xn∈{0，l} m X=>X EX= i=1 PrX≥1+=(uf
X = X n i=1 Xi E[X] = µ independent X1, X2,...,Xn 2 {0, 1} Pr[X (1 + )µ] e (1+) = (1+) µ Chernoff Bound