BFZ2011年元旦快乐PPT模板9689290469.ppt

1yx1x+y = z22当2 ?z 时,1)(?zFZ0)(?zfZ?????????????21,210,20,0)(zzzzzzzfZ或x+y = z当1?z < 2时,?????xzzdydx0111??????11)(1zdxxzz12/22???zzzzfZ??2)(z-11yx1?z?z)1()(??zzFZ当0 ?z < 1 时,????xzzZdydxzF001)(???zdxxz0)(2/2z?zzfZ?)(yx11x+y = z?z?z?????????????21,210,20,0)(zzzzzzzfZ或解法二用分布函数法)()(zYXPzFZ????????zyxdxdyyxf),(x+y = z当z < 0 时,0)(?zFZ1yx1???????dxxzfxfzfYXZ)()()(???10)(dxxzfY????????其他,01,1)(zxzxzfYz1z = x???10)(dxxzfY,20,0??zz或,10,10???zdxz,21,111????zdxzz-1= xx21例6已知(X ,Y ) ????????其他,010,10,1),(yxyxfZ = X + Y ,求f Z (z)解法一(图形定限法)??????其他,010,1)(xxfX??????其他,010,1)(yyfY显然X ,Y 相互独立,且独立,与设21XX),2,1)(,(~2?iNXiii??则~12XX?).,(222121??????N推广:更一般的情形是:,,,1相互独立若nXX??iNXiii)(,(~2??且不全为零时,则naa,,1?~1iniiXa??).,(2121iniiiniiaaN??????),,,1n?特别地,时,独立同正态分布),(,,21??NXXn?,11???niiXnX记则),(~2nNX??~1iniiXa??).,(1221????niiniiaaN??这表明正态分布也具有可加性。例例55:设:设X与Y是独立同分布的标准正态变量,求Z= X+ Y的分布.( ) ( ) ( )Z X Ydxf z f x f z x???? ??解:dx2 2( )2 21 12 2x z xe e? ???? ?????所以Z = X+ Y?N(0, 2).22[( ) ]2 412z zxe dx??????????22( )2124 21 12 2 122zxze e dx??????? ???????222( 2)12 2ze?????相互独立,与若YX即(,) ()()XYfxyfxfy??的密度为则Z() ( )()Z X Yfz fzyfydy???????或() ()( )Z XYfz fxfzxdx????? ??).(zfZ求另外,可用分布函数法}{)(zZPzFZ??}{zYXP?????????dy