※ 引述《[email protected] (我不知道)》之銘言： > 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. > 如果我定義p21=r2*p11, p22=r2*p12, ..., p2m=r2*p1m > ... > pn1=rn*p11, pn2=rn*p12, ..., pnm=rn*p1m > 讓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... 獨立的條件: (任一個皆可) (1) p_{ij} = p_{i.} p_{.j} (2) p_{j|i} = p_{ij}/p_{i.} 與 i 無關. > 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 > 不知道有沒有更快的方法? > 煩請指教~感謝~~~ -- ◢ 川◣ │││││ 您在找統計版嗎? 竭誠邀請您加入 Statistics! ▃▅▃▅▆ ◣││││ 無名小站 telnet://wretch.twbbs.org (cat▍_/ ▲ 、 ││ 成大計中站 telnet://bbs.ncku.edu.tw ▊ ▊Moon◤▍▍▄▂ │ 交大次世代 telnet://bs2.twbbs.org ▃─ _▍_ ◣▌▎▃▅ 盈月與繁星 telnet://ms.twbbs.org ▲ ◤ ￣ ◢▂▃ ＊Mooncat~ ★未經本人同意請勿轉載; 回覆請勿全文引用! -- 夫兵者不祥之器物或惡之故有道者不處君子居則貴左用兵則貴右兵者不祥之器非君子 之器不得已而用之恬淡為上勝而不美而美之者是樂殺人夫樂殺人者則不可得志於天下 矣吉事尚左凶事尚右偏將軍居左上將軍居右言以喪禮處之殺人之眾以哀悲泣之戰勝以 喪禮處之道常無名樸雖小天下莫能臣侯王若能守之萬物將自賓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將知止知止可以不殆譬道之在天 163.15.188.87海