[...]... ehorqj wr -1 - dqg 1 Zh vd| wkdw Qrwh wkdw qrqh ri wkh phpehuv lq - dqg duh Clvmrlqw - ehorqj wr dqg qrqh ri wkh phpehuv lq dqg wkdw wkhlu lqwhuvhfwlrq lv wkh hpsw| vhw -_ F ( Lq wklv fdvh wkh suredelolw| ri hlwkhu - HK rffxuulqj lv htxdo wr 5 ^- HK ` @ Golp " zkhuh wkh ^ v|pero vwdqgv iru wkh xqlrq suredelolw|= Li wzr suredelolwlhv1 Ilqdoo|/ ohw wkh hyhqw G- G G ri wzr vhwv1 @ 5 ^- ^ F +5,... 8NIIrvh wkh hyhqw - zdv wkh vhw ri doo vsdghv1 Wkhq - ( E,> 5> 6> 7> 8> 9> :> ;> 43> M > T> N j Qrz zh vd| wkdw Wkh hyhqw - rffxuv zkhqhyhu dq rxwfrph lv ri d wuldo lv frqwdlqhg lq -1 Lq wklv fdvh/ zkhqhyhu wkh rxwfrph ri d wuldo frqwdlqv d R/ wkh rxwfrph ehorqjv wr - dqg zh vd| wkdw - rffxuuhg1 Vr/ vxssrvh zh frqgxfwhg wkh deryh h{shulphqw "!> !!! wlphv/ dqg wkh hyhqw - rffxuuhg $!!!... GG $!!! ( "!!!! ( ! $ = Dv lqfuhdvhg wr lqqlw| +dqg dvvxplqj wkdw wkh fdugv duh idlu,/ wkhq wkh udwlr zrxog dssurdfk wkh q suredelolw| ri - G " 5 ^-` @G" - ( ( !=#& olp G % Qrwh wkdw wklv ghqlwlrq pdnhv vhqvh1 Vlqfh 5 ^- . alt="" Ω 1 1 52 x F(x) X s o 1 1 2 34 F(s) So x f(x) X 1 1 -1 X Y y {Y y} ≤ Y=2X+1 x=(y-1)/2 {X (y-1)/2} ≤ X Y y {Y y} ≤ Y=X 2 y -y ½ ½ F (x) X x µ σ 0 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x Fx(x) Rayleigh