例713求参数为p的0-1分布的最大似然估计 解 P{X=0}=1p P(x=m}=p(1-p)l吗(m=0,1) P{X=1}=p X=x}=p(1)xm→I(x,x2…,xn;p)=IIp(1-p)2 =p(-p)mhnL=C∑x)p+(m-∑x)m(1-P) dInL ∑x1n∑ 0m(1-p∑x+p(m-∑x)=0 dp 、￠ 1-p 解得p=∑Xm最大似然估计为 i=1 p X=X n例7.1.3 求参数为p的0-1分布的最大似然估计. 解. P{X=0}=1-p P{X=1}=p P{X=m}=pm(1-p)1-m  (m=0,1) P{X=x}=px (1-p)1-x = − − n i 1 x 1 x i i p (1 p) ( x )ln p (n x )ln(1 p) n i 1 i n i 1  i + − − = =  −  = = = − n i 1 i n i 1 i x n x p (1 p) 0 1 p n x p x n i 1 i n i 1 i = − − +   = = (1 p) x p(n x ) 0 n i 1 i n i 1 −  i + − = = = L(x1 ,x2 ,...,xn ;p) = lnL = = dp dlnL 解得 = = n i 1 Xi n 1 p 最大似然估计为 X X n 1 p n i 1 =  i = = 