《概率论》概率论与数理统计复习资料要点总结.doc

更多精彩华工学****资料请加华园文韵微信:scut_culture《概率论与数理统计》???????(1)BAABABBA????(2))()()()(BCACABCBACBA??????(3)))(()()()()(BA???????(4)BAABBABA????)(AP满足的三条公理及性质:(1)1)(0??AP(2)1)(??P(3)对互不相容的事件nAAA,,,21?,有????nkknkkAPAP11)()(?(n可以取?)(4)0)(??P(5))(1)(APAP??(6))()()(ABPAPBAP???,若BA?,则)()()(APBPABP???,)()(BPAP?(7))()()()(ABPBPAPBAP????(8))()()()()()()()(ABCPBCPACPABPCPBPAPCBAP?????????:(1)定义:若0)(?BP,则)()()|(BPABPBAP?(2)乘法公式:)|()()(BAPBPABP?若nBBB?,,21为完备事件组,0)(?iBP,则有(3)全概率公式:???niiiBAPBPAP1)|()()((4)Bayes公式:???niiikkkBAPBPBAPBPABP1)|()()|()()|(:BA,独立)()()(BPAPABP??(注意独立性的应用)更多精彩华工学****资料请加华园文韵微信::取有限或可列个值,iipxXP??)(满足(1)0?ip,(2)?iip=1(3)对任意RD?,????DxiipDXP:)(:具有概率密度函数)(xf,满足(1)1)(,0)(-??????dxxfxf;(2)????badxxfbXaP)()(;(3)对任意Ra?,0)(??),1(pBpXP??)1(,pqXP????1)0(ppq二项式分布),(pnBnkqpCkXPknkkn?,2,1,0,)(????,npnpqPoisson分布)(?P?,2,1,0,!)(????kkekXPk????几何分布)(pG?,2,1,)(1????kpqkXPkp12pq均匀分布),(baUbxaabxf????,1)(,2ba?12)(2ab?指数分布)(?E0,)(???xexfx???121?正态分布),(2??N2)(21)(???????xexf?2?)()(xXPxF??,具有以下性质(1)1)(,0)(??????FF;(2)单调非降;(3)右连续;(4))()()(aFbFbXaP????,特别)(1)(aFaXP???;(5)对离散随机变量,???xxiipxF:)(;(6)对连续随机变量,????xdttfxF)()(为连续函数,且在)(xf连续点上,)()('xfxF?)(x?记标准正态分布)1,0(N的分布函数,则有(1))0(??;(2))(1)(xx?????;(3)若),(~2??NX,则)()(?????xxF;更多精彩华工学****资料请加华园文韵