Concentration balls into bins coin flipping mps =1 m的3=3 ps=30 Tips =500 p5= balls =100,bins =100 hh业n山 0 08 08 40 80 8 100 balls =600,bins =100 06 06 06 06 20 10 urtbb 04 04 04 04 04 20 40 6080 100 balls =2000,bins =100 02 02 02 02 02 40 20 bhoi io.bw 20 406080 100 balm=5000,bln单=100 100 soLklTlrtu 20 Question: probability that X deviates more than 6 from expectation?
Concentration balls into bins coin flipping Question: probability that X deviates more than 𝛿 from expectation?
Chernoff Bounds Life in Los Angeles PROPORTION WHITE POPULATION URBAN STRESSES LOW HGH MED MED. MED an Chernoff 66 LOW 品
Chernoff Bounds Herman Chernoff
Chernoff Bounds For independent r..v.Xi,X2,·,Xn∈{0，l}, let=X and =E(),then: for any >0, X≥1+0m)s(-阿) for0<6<1, P(X≤(1-dm≤(a-西)
Chernoff Bounds
(Convenient)Chernoff Bounds For independent r..v.X1,X2,·,Xn∈{0,1} let=>X,and =E(X),then: for0≤6<1， P(X<1-ò)m)≤exp(-a了 P(X≥(1+o)u)≤exp fort≥2e, P(X≥t)≤2-t
(Convenient) Chernoff Bounds