F函数的一个重要性质是/(r+1)=r/() 证(+1)=Jxeh令n=c 则au=-exdb 令ν=x,利用分部积分公式 vau=uv 得/(+1)=-xex+「 rx'edx rr(r)
12 G-函数的一个重要性质是G(r+1)=rG(r), ( ) ( 1) , ( 1) 0 1 0 0 | | r r r x e rx e dx vdu uv udv v x du e dx r x e dx u e r x r x b a b a b a r x r x x G G G = + = - + = - = = - + = = + - - + - - - + - 得 令 利用分部积分公式 则 证 令
厂分布的数学期望 E5= xo(x)do X ( d(x) A(r)0 7(r)0 n(T(r+1) r厂(r)r ar(r n
13 G-分布的数学期望 lG l G G lG lG l l lG l G x l l r r r r r r t e dt r x e d x r x e dx r E x x dx r t r x r x = = = = + = = = + - + - + - + - ( ) ( ) ( 1) ( ) 1 ( ) 1 ( ) ( ) ( ) 1 ( ) ( ) 1 ( ) 0 0 0
厂分布的方差 E r+1- dx (r) 1 trte dt (r+2) 22(r)0 AT(r) (r+1)F(r+1)(r+1)r7(r)(r+1)r AT(r) 2() D=E2-(E) (r+1)y 2
14 G-分布的方差 2 2 2 2 2 2 2 2 2 2 0 1 2 0 2 1 ( 1) ( ) ( 1) ( ) ( 1) ( ) ( ) ( 1) ( 1) ( ) ( 2) ( ) 1 ( ) l l l x x x l G l G l G G l G G l G G l x l r r r r D E E r r r r r r r r r r r t e dt r x e dx r E r t r x r - = + = - = + = + = + + = = + = = = + + - + + -