※ 引述《[email protected] (我不知道)》之铭言： > 1.Consider the probability distribution of a bivariate discrete variable (X,Y) > may be represented as follows. > y1 y2 ... ym > x1 p11 p12 ... p1m p1. > x2 p21 p22 ... p2m p2. > ...xn pn1 pn2 ... pnm pn. > p.1 p.2 p.m > Prove that if every row is proportional to any other row, then X and Y are > independent. > 如果我定义p21=r2*p11, p22=r2*p12, ..., p2m=r2*p1m > ... > pn1=rn*p11, pn2=rn*p12, ..., pnm=rn*p1m > 让every row is proportional to any other row > =>p2.=r2(p11+p12+...+p1m)=r2*p1. > ... > pn.=rn(p11+p12+...+p1m)=rn*p1. ==> (1+r_1+...+r_n)p_{1.} = 1 > =>p.1=p11(1+r2+...+rn) > ... > p.m=p1m(1+r2+...+rn) ==> p_{.j} = p_{1j}(1/p_{1.}) ==> p_{ij} = r_i p_{1j} = r_i p_{1.} p_{.j} = p_{i.} p_{.j} > 然後我就卡住了... 独立的条件: (任一个皆可) (1) p_{ij} = p_{i.} p_{.j} (2) p_{j|i} = p_{ij}/p_{i.} 与 i 无关. > 2.Suppose that X1,...,Xn from a random sample of size n from the uniform > distribution on the interval (0,1) and that Yn=max{X1,...,Xn}. Find the > smallest value of n such that > P[Yn>=0.99]>=0.95 P[Yn<a] = P[X1<a,...,Xn<a] > 我的想法是先找出Yn的pdf > 再代入P[Yn>=0.99]>=0.95 > 求出最小的n > 不知道有没有更快的方法? > 烦请指教~感谢~~~ -- ◢ 川◣ │││││ 您在找统计版吗? 竭诚邀请您加入 Statistics! ▃▅▃▅▆ ◣││││ 无名小站 telnet://wretch.twbbs.org (cat▍_/ ▲ 、 ││ 成大计中站 telnet://bbs.ncku.edu.tw ▊ ▊Moon◤▍▍▄▂ │ 交大次世代 telnet://bs2.twbbs.org ▃─ _▍_ ◣▌▎▃▅ 盈月与繁星 telnet://ms.twbbs.org ▲ ◤ ￣ ◢▂▃ ＊Mooncat~ ★未经本人同意请勿转载; 回覆请勿全文引用! -- 夫兵者不祥之器物或恶之故有道者不处君子居则贵左用兵则贵右兵者不祥之器非君子 之器不得已而用之恬淡为上胜而不美而美之者是乐杀人夫乐杀人者则不可得志於天下 矣吉事尚左凶事尚右偏将军居左上将军居右言以丧礼处之杀人之众以哀悲泣之战胜以 丧礼处之道常无名朴虽小天下莫能臣侯王若能守之万物将自宾天地相合以降甘露民莫 之令而自均始制有名名亦既有夫亦将知止知止可以不殆譬道之在天 163.15.188.87海