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數學與統計 大學

第二題的d的積分範圍要怎麼設

6 Kx, lo, 14) 1. (10 points) How many even numbers can be formed from the digits 9, 1,4,5,6, and 9 if each digit can be used only once? 2. (50 points) Let X and Y denote the lengths of life, in years, of two components A and B, respectively, ş! x2 in an electronic system. If the joint density function of these variables is 64 0<x<1-ycl EX,Y) Rx hy 0 < x <1.0<x<1-x: f(x, y) = elsewe jey.301-4)*84f CX74 3 Rxdy * 了 1' Jay You Determine the value k; FED ECX) = 86 x 6xci->)dy cy) 3(1-2) ² (b) Find the marginal distributions, expected values, variances, and covariance of X and Y; dy= 1 (C) Determine whether X and Y are dependent or independent; X(d) Find the probability that the length of life of component A is less than that of component B; X(e) Find the probability that the length of life of component A is greater than one year, given the ar length of life of component B is equal to two year. xcy 1313. (10 points) The probability that a flight departs on time is 0.3; the probability that it arrives on time is 0.3; and the probability that it departs and arrives on time is 0.1. Find the probability that it arrives on time, given that it did not depart on time. ex oin 4. (20 points) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution -8x76 / le = 1- e 11-e dx x ZO; dv=e 0, f(x) = f'(X) = x < 0. 8 e V= 1 84 (a) Find the probability of waiting less than 10 minutes between successive speeders; hind the wyerane waiting time between successiye speeders spotted by a radar unit. 013-0il u=X -8X -81 -8% ge

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商業與管理 大學

財管題目,求解😭😭😭

@ 今天,小陳正在慶祝她的 40 歲生日。她的願望是希望在 65 歲退休時,退休後 的 20 年間,每年生日時都能從儲著帳戶中提出$240,000。第一次提款時間是她 的 66 歲生日。小陳打算參加兆豐銀行零存整付專案 (年利率 2%) ,每年生日 時都存入一筆等額現金到此專案帳戶 ,做為退休基金之用。 (1) 如果小陳從 40 歲開始存款,一直到 65 歲 (最後一筆存款是 65 歲生日) ,請問 她每年要存入多少錢才能支應她的退休需求 ? (可先找出以下條件:預計幾年後 退休 ? 退休後每年可領金額 ? 退休儲蓄金可使用年限? ) (2) 假設小陳剛剛很幸運地中了大樂透,所以她決定要改變計畫,不要每年存入等 額的現金,而是在40歲生日時直接存入一大筆可以滿足她退休計畫的錢。請問 大樂透獎金至少要多少錢才夠呢 ? 如果大樂透獎金為$1,500,000 , 請問足以支 應退休計畫嗎?若是可以,請問小陳退休後每年可提領的金額增加多少? 若是不 足以支應,請問小陳每年要再存入多少錢才能支應她的退休需求? ( 假設不考慮 稅賦等影響因素 ) (3) 假設小陳的公司提出員工分紅計畫 ,每年會有$12,500 元分紅直接存在她的儲蔡 帳戶。此外,小陳預期在她 55 歲生日時,可從一筆家族信託基金領到$120,000, 到時她也會把這筆基金直接存到她的退休金帳戶。請問,若有分紅計畫和家族 信託基金的幫助,小陳每年應該還要存入多少錢,來支應她的退休計畫呢?

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