【正文】 cted sample of 20 Vermont residents, with x = the number sampled who were boating participants that year, determine: a. E(x) = b. P(x ? 8)= c. P(x = 10)= d. P(x = 12)= e. P(7 ? x ? 13)= Answers: a. E(x) = n p = 20 x = 10 b. P(x ? 8) = c. P(x = 10) = d. P(x = 12) = e. P(x ? 13) = , P(x ? 6) = P(7 ? x ? 13) = – = Using Microsoft Excel b. P(x ? 8) In a cell on an Excel worksheet, type =BINOMDIST(8,20,true) and you will see the answer: c. P(x = 10) In a cell on an Excel worksheet, type =BINOMDIST(10,20,false) and you will see the answer: = d. P(x = 12) In a cell on an Excel worksheet, type =BINOMDIST(12,20,false) and you will see the answer: = e. P(7 ? x ? 13) In a cell on an Excel worksheet, type =BINOMDIST(13,20,true) BINOMDIST(6,20,true) and you will see the answer: = 512 Main Content ? (5)Mean and standard definition ? The probability distribution for a discrete random variable defines the probability of a discrete value x. – Mean: 181。 = E(x) = – Variance: s2 = E[(x – 181。)2] = ? Binominal distribution ? Mean E(x)=np ? Variance s2=npq ()xp x?2( ) ( )x p x???513 Terminologies ? Discrete random variable ? Binomial probability distribution ? Continuous random variable ? Counting rule for binations ? Binomial formula 513 Terminologies ? Expected value of a discrete random variable ? Expected value of a binomial distribution ? Standard deviation of a discrete random variable ? Standard deviation of the binomial distribution 514 After school extend ? catalog sales ? Usbio introduction 52 Other Discrete Probability Distributions ? 521 Vocabularies 詞匯 ? 522 Main Content 主要內(nèi)容 ? 523 Terminologies 專業(yè)詞匯 ? 524 After school extend 課外擴(kuò)展 521 Vocabularies ? Vermont ? A state of the northeast United States bordering on Canada. It was admitted as the 14th state in 1791. Explored by Samuel de Champlain in 1609, the region was first permanently settled by the British in 1724. Claims to the area were relinquished by Massachusetts in 1781, New Hampshire in 1782, and New York in 1790. Montpelier is the capital and Burlington the largest city. Population, 564,964. ? 佛蒙特州：美國東北部的一個(gè)州，與加拿大接壤。它于1791年被接受為美國的第十四個(gè)州。 1609年塞繆爾 德 查普蘭勘探了這個(gè)地區(qū)， 1724年英國人在該地區(qū)永遠(yuǎn)定居了下來。馬薩諸塞州、新罕布什爾州和紐約州于 1781年、1782年和 1790年相繼放棄了對這個(gè)地區(qū)的權(quán)利。該州首府為蒙彼利埃，伯林頓是最大的城市。人口 564,964 521 Vocabularies ? downsize ? vt. To make in a smaller size減小 (汽車的尺寸 , 重量和耗油量 ) ? cars that were downsized during the gasolineconscious 197039。s。 ? 在汽油短缺的七十年代以較小尺寸制造的小汽車 ? a corporation that downsized its personnel in response to a poor economy. ? 因經(jīng)濟(jì)不景氣而裁員的股份有限公司 521 Vocabularies ? lay ? lay aside： To give up。 abandon:放棄；拋棄： ? Eg. lay aside all hope of ? lay off： To terminate the employment of (a worker), especially ：停止雇用（工人），尤指暫時(shí)性的 ? lay on： To apply (something) by or as if by spreading (it) onto a flat surface:帶有：將某物抹在或好象涂在一平整表面上： ? Eg. laid on a thick Southern 南方口音 521 Vocabularies ? chuckhole(馬路上的坑或凹處 )。 ? segment(段，節(jié)，片斷，分割 )。 ? strech(伸展、一段路程、時(shí)間 )。 ? Vermont(佛蒙特州 )。 ? acme(頂點(diǎn)、極致 )。 ? vending machine(自動(dòng)售貨機(jī) ,自動(dòng)販賣機(jī) )。 ? printer(印刷工，打印機(jī) )。 ? reinspect(再考慮、重新考察 )。 ? glance(掃視、匆匆一看 )。 ? Hewlettpackard LaserJet printer ? 惠普激光打印機(jī) 522 Main Content ? the Poisson distribution ? (1) Definition ? The Poisson distribution defines the probability that an event will occur exactly x times over a given span of time, space, or distance. ? The possible counts are the integers. 522 Main Content ? the Poisson distribution ? (2) Assumptions ? ① is the average number of success in a segment of unit size. ? ② the probability of x success in a segment is the same for all segments of the same size. ? ③ what happens in one segment has no influence on any nonoverlapping segment. ? ④ we imagine dividing time or space into tiny subsegment. Then the chance of more than one success in a subsegment is negligible and the chance of exactly one success in a tiny subsegement of length t is . ?t?522 Main Content ? the Poisson distribution ? (3) Formular ? Where: t=size of the segment of interest ? x= number of successes in the segment of interest ? =expected number of success in s segment of unit size ? e= base of the natural logarithm system(..) ()()!xttepx x?? ??()()!tepxx?? ???522 Main Content – The Poisson distribution example, During the 12 . – 1 . noon hour, arrivals at a curbside (路旁的 )banking machine have been found to be Poisson distributed with a mean of persons per minute. If x = number of arrivals per minute, determine: – a. E(x) = ? = – b. 0 1 . 3 0 . 2 7 2 5( 1 . 3 ) ( 2 . 7 1 8 2 8 )( 0 ) 0 . 2 7 2 50! 1Px ?? ? ? ?522 Main Content c. – d. P(x ? 2) = from poisson Table, ? = , k = 2 – If use excel – P(x = 0) In a cell in an Excel spreadsheet, type =POISSON(0,false) P(x = 1) type =POISSON(1,false) – P(x ? 2) type =POISSON(2,true) 1 1 . 3 0 . 3 5 4 3( 1 . 3 ) ( 2 . 7 1 8 2 8 )( 1 ) 0 . 3 5 4 31! 1Px?? ? ? ?522 Main Content ? the Poisson distribution ? (4) Mean and standard defi