[问题1] consider an urn that initially contains one red ball and one black ball. At each time n=1,2…,a ball is drawn, and it and another two balls of the same color are placed back into the urn.Thus,after n draws the urn contains 2n+2 balls. LetYn be the number of balck in the urn after n draws and let Xn=Yn/(2n+2) Prove the identity E(Xn+1|Xn=x)=x ,n=1,2… [问题2] 令汽车之行驶速度为μ(km/hr)，对警察而言，此为一未知数，须藉助测速器的 测量值X来估计。已知X的分配为N(μ,σ^2 )，其中标准差σ=4km/hr。 原则上超过限速便算违规，然顾及测速器之可能误差，除非「显着」超速，否则 不会开罚单。假设在限速100km/hr下，照相测得110km/hr或以上才会开出罚单。 (a)写出所检定的两个假说(hypothesis)及其rejection rule (b)此检定的maximum type Ⅰ error rate是多少？ (c)今某人实际上开106km/hr而被照相，试问他会被开罚单的机率为何？ (d)如果测速器是连拍4次，取平均後若超过(100+k)km/hr才开罚单。 在此情形下，要控制type Ⅰerror rate<0.001，则k最小可取到多少？ [问题3] Let X1,...Xn be independently and identically distributed with density f(x)=(1/σ)*exp{-(x-μ)/σ} ,x>μ,-∞<μ<∞,σ^2>0 = find mle of σ^2 ============================================================================ 麻烦版上大大帮我解答一下 拜托了~~ 感谢~~ --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 218.174.189.5 ※ 编辑: brucejune 来自: 218.174.189.5 (04/18 19:32)