【正文】 nable from the formula b(x。n,p) of the binomial distribution or from Table when n is small. In addition, binomial probabilities are readily available in many software puter packages. However, it is instructive to learn the relationship between the binomial and normal distribution. In section we illustrated how the Poisson distribution can be used to approximate binomial probabilities when n is quite large and p is very close to 0 or 1. both the binomial and Poisson distributions are discrete. 534 After school extend ? normal approximation to the binomial（接前頁） ? The first application of a continuous probability distribution to approximate probabilities over a discrete sample space is demonstrated by example , where the normal curve was used. The normal distribution is often a good approximation to a discrete distribution when the latter takes on a symmetric bell shape. From a theoretical point of view, some distributions converge to the normal as their parameters approach certain limits. The normal distribution is a convenient approximating distribution because the cumulative distribution function is so easily tabled. 54 Other Continuous Probability Distributions ? 541 Vocabularies 詞匯 ? 542 Main Content 主要內(nèi)容 ? 543 Terminologies 專業(yè)詞匯 ? 544 After school extend 課外擴展 ? 545 Literature 文獻導讀 541 Vocabularies ? elapse ? To slip by。 pass:悄悄過去；消逝： ? Weeks elapsed before we could start renovating.(翻譯 ) ? 幾周過去后我們才開始修復 ? n.（名詞） ? Passage。 lapse:過去；逝去： ? met again after an elapse of many years.(翻譯 ) ? 多年后又相逢 541 Vocabularies ? drivein ? (1) establishment designed to permit customers to remain in their motor vehicles while being ：顧客接受服務時可不下車的營業(yè)場所或娛樂設施（如免下車餐館 , 免下車電影院） ? [美 ](讓顧客不下汽車即可吃飯、辦事、看戲等的 )路旁餐館[銀行 ], 露天電影院 ? 39。s eat at the drivein “免下車” 餐館吃飯吧。 ? (2)；路邊服務式的 (飯店、電影院等 )。 露天營業(yè)式的 ? (3)drive in趕進 , 敲進 541 Vocabularies ? teller ? n.(1)One who tells:敘述者： ? teller of tall ? (2)A bank employee who receives and pays out money.出納員：接受和支付錢款的銀行雇員 ? (3)A machine, as in a bank, that automatically conducts personal financial transactions in response to a client39。s use of a coded ：銀行使用的能對委托人持用的有密碼的卡片作出反應并自動進行個人財產(chǎn)交易的機器 ? (4)A person appointed to count votes in a legislative ：被指派在議會中數(shù)票的人 541 Vocabularies ? teller ? automatic(al) teller 銀行自動機 ? coupon teller 息票付款員 ? deposit teller 收款員 ? discount tellers 貼現(xiàn)人員 ? exchange teller 匯兌員 , 匯兌股人員 ? moisture teller 水分快速測定儀（ moisture 潮濕，濕氣） ? note teller (銀行 )票據(jù)員 ? paying teller 付款員 ? receiving teller 收款員 541 Vocabularies ? interval ? （ 1） A space between two objects, points, or units. ? 間隔，空隙：兩上物體、點、或構(gòu)件之間的空間 ? （ 2） Mathematics A set of numbers consisting of all the numbers between a pair of given numbers. ? 【 數(shù)學 】 區(qū)間：由一對已知數(shù)之間所有數(shù)組成的一組數(shù) ? A set of numbers consisting of all the numbers between a pair of given numbers and including the called ? closed interval 閉區(qū)間 ? A set of numbers consisting of all the numbers between a pair of given numbers but not including the called ? open interval 開區(qū)間 542 Main Content ? the uniform probability distribution ? Where: f(x)=value of the density function at any x value。 ? a=lower limit of the interval from a to b。 ? b=upper limit of the interval from a to b。 1. . . . . .()0 . . . . . . . . . . .if a x bfx bao th e r w is e? ????????542 Main Content ? Mean and standard deviation of a uniform distribution (均勻分布的均值和標準差 ): ? Mean (expected value): ? Standard deviation: ? Where: a=lower limit of the interval from a to b。 b=upper limit of the interval from a to b。 () 2abEx ? ???2()12bas ??542 Main Content ? ? A continuous random variable that is exponentially distributed has the probability density function given by ? Where: e=。 ? 1/? = the mean time between events (??0). 0,)( ?? ? xexf x??? Relationship between the Poisson and Exponential Distributions 泊松分布描述特定時間或空間間隔中，事件發(fā)生的次數(shù)服從的分布 (If) the Poisson distribution provides an appropriate description of the number of occurrences per interval (If) the exponential distribution provides an appropriate description of the length of the interval between occurrences () !x efx x?? ??Example 假設 1小時內(nèi)到達洗車行的汽車數(shù)服從泊松分布，均值為每小時10輛。 ? 則每小時有 x輛到達的概率函數(shù)是 兩次到達間隔的平均時間是 ? 兩次到達間隔時間的概率密度是 1010() !x efx x??1 0 . 110 ?小 時 小 時 / 輛輛/ 0 . 1 1 010 . 1( ) 1 0xxf x e e????543 Terminologies ? Continuous uniform distribution ? Mean and standard deviation of a uniform distribution ? Exponential distribution ? Exponential probability 544 After school extend 545 Literature 各種分布練習題 ? 麥田中平均每 10平方米有一株雜草，現(xiàn)在要問每 100平方米麥田中無雜草、有 1株雜草、以及有 5株以上雜草的概率各為多少？ ? 提示：泊松分布 ? 答案： ， ， 各種分布練習題 ? 由人口統(tǒng)計資料知道某地區(qū)女孩的出生概率為 ，問在第 10個女孩出生時，已出生了 20個男孩的概率是多大？ ? 提示：負二項分布 ? 答案：.=negbinomdist(20,10,) 各種分布練習題 ? 已知婦女患色盲者占 %。試求 ? 1）為發(fā)現(xiàn)一例患色盲者，至少要檢查 25個婦女的概率。 ? 2）為使發(fā)現(xiàn)一例患色盲者的概率不小于 ，至少要對多少婦女的辨色力進行檢查？ ? 提示：幾何分布 ? 答案： ， 920人 各種分布練習題 ? 在 50個零部件中，已知有 5個不合格，如果不重置隨機抽取 4個零件。問： ? 1） 4個樣品中剛好有一個不合格的概率是多少？ ? 2）不超過 2個不合格零件的概率是多少？ ? 提示：超幾何分布 ? 答案： ， End of Chapter 5