Binomial Distribution

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- 1 - CHƯƠNG I GIỚI THIỆU VỀ CÔNG FPT DISTRIBUTION 1.1.Qúa trình hình thành và phát triển của FPT DISTRIBUTION COMPANY (FDC): Công ty Phân phối FPT đã và đang dẫn đầu thị trường công nghệ thông tin (CNTT) và viễn thông tại Việt Nam, luôn sát cánh cùng các đối tác và hệ thống đại lý của mình mang đến cho người tiêu dùng Việt Nam những sản phẩm CNTT mới nhất, đa dạng về chủng loại và hoàn hảo về chất lượng. Là một công ty thành viên của Tập đoàn FPT, được chính thức thành lập từ ngày 13/4/2003 với trụ sở chính đặt tại Hà Nội và chi nhánh ở Tp. Hồ Chí Minh, Đà Nẵng, Cần Thơ, công ty luôn tự hào là đơn vị có thành tích kinh doanh nổi bật trong tập đoàn, với doanh thu năm 2007 vượt mức 516 triệu USD và tốc độ tăng trưởng hàng năm đạt hơn 59%. Hiệu quả hoạt động của Công ty Phân Phối FPT đã được khẳng định bởi chứng chỉ hệ thống quản lý chất lượng đạt tiêu chuẩn ISO9001:2000. Công ty Phân phối FPT đã chứng minh được vị thế số 1 trong lĩnh vực phân phối các sản phẩm CNTT và Viễn thông trên thị trường Việt Nam. Công ty Phân phối FPT có cơ cấu tổ chức chặt chẽ và thống nhất trên toàn quốc với đội ngũ nhân viên đông đảo, nhiệt tình, năng động, sáng tạo, có trình độ chuyên môn và năng suất lao động cao, trong đó trên 92% số nhân viên có kinh nghiệm hoạt động trong lĩnh vực CNTT, viễn thông và phân phối. Hệ thống thông tin đóng vai trò hết sức quan trọng trong thành công của Công ty, trong đó phải kể đến hệ thống thông tin tài chính và thông tin quản lý: phần mềm kế toán Oracle, FIFA (FPT Information Finance Architecture), MIS (Management Information System), SCM (Supply Chain Management), CRM (Customer Relationship Management), HRM (Human Resource Management), FDC Inside . Với những thế mạnh sẵn có cùng tôn chỉ hướng tới khách hàng, Công ty Phân phối FPT cam kết tiếp tục mang đến cho khách hàng của mình những giá trị gia tăng, giữ vững niềm tin và uy tín với các đối tác, tiếp tục đứng vững trên thị trường trong nước và vươn ra thị trường nước ngoài -Tên giao dịch : FPT Distribution -Ngày thành lập : 13/04/2003 (kết hợp từ 3 trung tâm phân phối của FPT) -Trụ sở : 298G Kim Mã, Quận Ba Đình, Hà Nội -Vốn đầu tư : 516 triệu USD Binomial Distribution Binomial Distribution By: OpenStaxCollege There are three characteristics of a binomial experiment There are a fixed number of trials Think of trials as repetitions of an experiment The letter n denotes the number of trials There are only two possible outcomes, called "success" and "failure," for each trial The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial p + q = The n trials are independent and are repeated using identical conditions Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial Another way of saying this is that for each individual trial, the probability, p, of a success and probability, q, of a failure remain the same For example, randomly guessing at a true-false statistics question has only two outcomes If a success is guessing correctly, then a failure is guessing incorrectly Suppose Joe always guesses correctly on any statistics true-false question with probability p = 0.6 Then, q = 0.4 This means that for every true-false statistics question Joe answers, his probability of success (p = 0.6) and his probability of failure (q = 0.4) remain the same The outcomes of a binomial experiment fit a binomial probability distribution The random variable X = the number of successes obtained in the n independent trials The mean, μ, and variance, σ2, for the binomial probability distribution are μ = np and σ2 = npq The standard deviation, σ, is then σ = √npq Any experiment that has characteristics two and three and where n = is called a Bernoulli Trial (named after Jacob Bernoulli who, in the late 1600s, studied them extensively) A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials At ABC College, the withdrawal rate from an elementary physics course is 30% for any given term This implies that, for any given term, 70% of the students stay in the class for the entire term A "success" could be defined as an individual who withdrew The 1/17 Binomial Distribution random variable X = the number of students who withdraw from the randomly selected elementary physics class Try It The state health board is concerned about the amount of fruit available in school lunches Forty-eight percent of schools in the state offer fruit in their lunches every day This implies that 52% not What would a "success" be in this case? a school that offers fruit in their lunch every day Suppose you play a game that you can only either win or lose The probability that you win any game is 55%, and the probability that you lose is 45% Each game you play is independent If you play the game 20 times, write the function that describes the probability that you win 15 of the 20 times Here, if you define X as the number of wins, then X takes on the values 0, 1, 2, 3, , 20 The probability of a success is p = 0.55 The probability of a failure is q = 0.45 The number of trials is n = 20 The probability question can be stated mathematically as P(x = 15) Try It A trainer is teaching a dolphin to tricks The probability that the dolphin successfully performs the trick is 35%, and the probability that the dolphin does not successfully perform the trick is 65% Out of 20 attempts, you want to find the probability that the dolphin succeeds 12 times State the probability question mathematically P(x = 12) A fair coin is flipped 15 times Each flip is independent What is the probability of getting more than ten heads? Let X = the number of heads in 15 flips of the fair coin X takes on the values 0, 1, 2, 3, , 15 Since the coin is fair, p = 0.5 and q = 0.5 The number of trials is n = 15 State the probability question mathematically P(x > 10) Try It A fair, six-sided die is rolled ten times Each roll is independent You want to find the probability of rolling a one more than three times State the probability question mathematically P(x > 3) 2/17 Binomial Distribution Approximately 70% of statistics students their homework in time for it to be collected and graded Each student does homework independently In a statistics class of 50 students, what is the probability that at least 40 will their homework on time? Students are selected randomly a This is a binomial problem because there is only a success or a , there are a fixed number of trials, and the probability of a success is 0.70 for each trial a failure b If we are interested in the number of students who their homework on time, then how we define X? b X = the number of statistics students who their homework on time c What values does x take on? c 0, 1, 2, …, 50 d What is a "failure," in words? d Failure is defined as a student who does not complete his or her homework on time The probability of a success is p = 0.70 The number of trials is n = 50 e If p + q = 1, then what is q? e q = 0.30 f The words "at least" translate as what kind of inequality for the probability question P(x 40) f ... - 67 - CHARACTERISTICS AND DISTRIBUTIONS OF NITROUS OXIDE-PRODUCING DENITRI- FYING FUNGI IN NATURAL ENVIRONMENTS K. Oishi and T. Kusuda Department of Civil Engineering, Faculty of Engineering, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan Abstract Tea field soils, and sediments of an irrigation pond and a tidal river, in which a variety of organic matter was supplied as energy sources, were collected. The activities of bacterial and fungal denitrifications in these samples were determined. Denitrifying fungi in all of these samples produced N 2 O from nitrate and nitrite as a final product, whereas denitrifying bacteria produced N 2 . Nitrous oxide produced by fungi was reduced to N 2 by bacteria. The fungal denitrification potentials were the highest in the submerged litter on the pond sediment, followed by the farmyard manure-amended soil, the inorganic fertilizer-amended soil, the litter-free pond sediment, and the tidal river sediment. The enrichments of denitrifying fungi in natural envi- ronments were related with the distributions of the organic material such as straws and litter. The contributions of fungal denitrification to total denitrification were large in soil environments, especially in the farmyard manure-amended soil, and were small in aquatic environments such as the sediments of pond and river. The pH in situ was not related with the fungal denitrification potentials. Keywords fungal denitrification; bacterial denitrification; nitrous oxide; organic matter; sediments; soils Introduction Fungi generally are found in lakes, ponds, rivers, estuaries, marine, wastewater, and soils. Despite their wide occurrence, little attention has been given to the presence and ecological significance of fungi. Especially, characteristics and contributions of fungal denitrification in natural environments are poorly understood. Deni- trification is a process in which nitrite and/or nitrate are reduced to N 2 gas through N 2 O. The process has been considered to be mainly caused by bacteria. However, pure culture experiments have shown that fungi such as Fusarium sp., Trichoderma hamatum, Chaetomium sp., Gibberella fujikuroi etc., can reduce nitrite and several strains can reduce nitrate as well, but the final product is mainly N 2 O rather than N 2 ( Bleakley and Tiedje, 1982; Burth and Ottow, 1983; Shoun and Tanimoto, 1991; Shoun et al., 1992). The distributions of denitrifying fungi, which produce N 2 O as a final product, would be ecologically important to understand the contribution of natural systems to the atmospheric concentration of N 2 O. Previous studies have been con- ducted with pure cultures of fungi. However, the characteristics and distributions of denitrifying fungi in natural environments are unknown. In this study, tea soils, and the sediments of an irrigation pond and a tidal river, to which different types of organic matter were supplied, were collected. The final products of fungal denitrification in these soils and sediments were determined, and the distribution of denitrifying fungi in natural system was estimated. Materials Tea field soils Soils were collected at the surface (0-10cm) in two tea fields. One was mainly amended with a farmyard manure (organic soil), and the other with inorganic fertilizer Journal of Water and Environment Technology, Vol.3, No.2, 2005 - 169 - INFLUENCE DISTRIBUTIONS OF ACID DEPOSITION IN MOUNTAINOUS STREAMS ON A TALL CONE-SHAPED ISLAND, YAKUSHIMA S. Ebise* and O. Nagafuchi** *Dept. of Civil and Environmental Engineering System, Setsunan University, 17-8 Ikeda-Nakamachi, Neyagawa, Osaka, 572-8508, Japan **Dept. of Environmental System, Chiba Institute of Science, 3 Shiomi, Choshi, Chiba 288-0025 ABSTRACT Yakushima, facing at 800 km east of Shanghai in the East China Sea, is a tall cone-shaped island with seven exceeding 1800 m peaks. The prevailing winds of westrelie on the island blow mostly fromnorthwest and west. It has been exposed to acid rain of pH 4.7 and precipitation 8000 mm in the central highland. More than sixty mountainous streams were observed at downstream points seasonally for past twelve years. The alkalinity of streamwaters in the southwestern part was lower than others. The concentrations of SO 4 2- in the northwestern part were higher than others. The high concentrations of SO 4 2- , dissolved SiO 2 and other ions in the southwestern part with high canopy density of evergreen broadleaved forest were caused by higher air temperature, less rainfall and higher evapotranspiration than other parts. The alkalinity, pH and EC in the catchment of north stream in the upstream branch of the R. Anboh became lower than those in the catchment of south stream. The height of catchment boundaries, the direction of the main axis of a catchment and the prevailing winds govern the influence of acid deposition on water quality of branch streams. KEYWORDS Acid deposition; mountainous stream; influence distribution; cone-shaped; prevailing wind INTRODUCTION Yakushima, an island lying 800 km east of Shanghai on the boundary between the Pacific Ocean and East China Sea (Fig. 1), is a World Heritages Area and a National Park of Japan. Yakushima is famous for its yaku-sugi (Crytomeria japonica), one of which, called Jomon-sugi, is the oldest living organism in Japan. The prevailing winds on the island were northwestern (strongly so in winter) and western except during the short typhoon season, when the wind comes from the southeast. Consequently, Yakushima is exposed to acid deposition with an annual mean pH of 4.7 (MOE, 2004). The annual precipitation ranges 4300 mm at the coast to above 8000 mm in the central highland where seven peaks exceeds 1800 m. The tallest peak is Mt. Miyanouradake at 1935 m. The island has a steep mountainous landform and is covered with a thin soil layers overlying granite. Therefore, the soil’s ability to neutralize acid deposition is very weak (Ebise, 1996). Journal of Water and Environment Technology, Vol.3, No.2, 2005 - 170 - Figure 1 Yakushima Island and main rivers All 14,000 residents of the island live on the coast. There are no sources of artificial pollutants in the mountains, where the only visitors are mountain climber and backpackers. Back-trajectory and Pb-isotope trace methods show that most of the acid deposition coming from the Asia Continent is transported overseas by the prevailing westerlies in the upper air region, until it strikes the high mountains on the island. The major species in the acid deposition is sulfuric acid (Nagafuchi et al. 1995, 2001a, 2001b). The pH of wet deposition tends to be lower in Journal of Water and Environment Technology, Vol.4, No.1, 2006 - 61 - Effect of urban emissions on the horizontal distribution of metal concentration in sediments in the vicinity of Asian large cities T. Urase 1* , K. Nadaoka 2 , H. Yagi 2 , T. Iwasa 1 , Y. Suzuki 1 F. Siringan 3 , T. P. Garcia 4 , T. T. Thao 5 1: Dept. of Civil Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8552 Japan. *: Corresponding author. turase@fluid.cv.titech.ac.jp , +81-3-5734-3548 2: Dept. of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8552 Japan. 3: National Institute of Geological Sciences, University of the Philippines, 1101 Diliman, Quezon City, Philippines 4: Dept. Civil Engineering, College of Engineering, Technological University of the Philippines, Manila, Philippines 5: Department of Analytical Chemistry, Hanoi University of Science, 19- LeThanh Tong street, Hanoi, Vietnam Abstract: Metal contents of sediments in Manila Bay – Laguna Lake watershed in the Philippines were measured and detailed horizontal distribution was obtained. The distribution of zinc and lead concentration in Manila Bay clearly shows the effect of anthropogenic contamination and it was explained by the diffusion of lead and zinc rich anthropogenic particles discharged from Pasig River. The sediments in Laguna Lake were mostly natural particulate matters from surrounding mountains and they contained 20 mgPb/kg and 100 mgZn/kg, while the sediment taken at the heavily polluted branches of the Pasig River contained as high as 88 mgPb/kg and 310 mgZn/kg. The lead and zinc concentrations in the sediments of Manila Bay – Laguna Lake watershed were compared with those in the mouth of the Tama River, Tokyo, where the faster deposition of coarser natural origin particles and slower deposition of lead and zinc rich anthropogenic particles determined the sediment concentration. The comparison was also made with Hanoi City, Vietnam. In spite of the difference in time when leaded gasoline was prohibited, the difference in the lead concentrations of roadside deposits and sediments was not obvious in the vicinity of these three target cities. This is probably due to dilution by a large amount of suspended solids conveyed by the Pasig River in the case of the Philippines. Storm water runoff containing roadside deposits and discharge of untreated wastewater were identified as factors increasing zinc and lead concentrations of sediments in receiving waters based on the measurements on roadside deposits and the estimation of the contribution of untreated wastewater. Keywords: Laguna Lake; lead; Manila Bay; sediment; wastewater; zinc. Introduction Asian cities generally have large populations. Human activities and their impacts on natural environments are concentrated in the vicinity of urban regions. High precipitation in Asian regions results in erosion of land and induces urban runoff during wet weather days. A large amount of particulate matters having natural and anthropogenic sources flows into receiving watersheds. Incomplete sewer problems such as low coverage and 7 CHAPTER The Binomial Distribution Introduction Many probability problems involve assigning probabilities to the outcomes of a probability experiment. These probabilities and the corresponding outcomes make up a probability distribution. There are many different probability distributions. One special probability distribution is called the binomial distribution. The binomial distribution has many uses such as in gambling, in inspecting parts, and in other areas. 114 Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use. Discrete Probability Distributions In mathematics, a variable can assume different values. For example, if one records the temperature outside every hour for a 24-hour period, temperature is considered a variable since it assumes different values. Variables whose values are due to chance are called random variables. When a die is rolled, the value of the spots on the face up occurs by chance; hence, the number of spots on the face up on the die is considered to be a random variable. The outcomes of a die are 1, 2, 3, 4, 5, and 6, and the probability of each outcome occurring is 1 6 . The outcomes and their corresponding probabilities can be written in a table, as shown, and make up what is called a probability distribution. Value, x 123456 Probability, P(x) 1 6 1 6 1 6 1 6 1 6 1 6 A probability distribution consists of the values of a random variable and their corresponding probabilities. There are two kinds of probability distributions. They are discrete and continuous.Adiscrete variable has a countable number of values (countable means values of zero, one, two, three, etc.). For example, when four coins are tossed, the outcomes for the number of heads obtained are zero, one, two, three, and four. When a single die is rolled, the outcomes are one, two, three, four, five, and six. These are examples of discrete variables. A continuous variable has an infinite number of values between any two values. Continuous variables are measured. For example, temperature is a continuous variable since the variable can assume any value between 108 and 208 or any other two temperatures or values for that matter. Height and weight are continuous variables. Of course, we are limited by our measuring devices and values of continuous variables are usually ‘‘rounded off.’’ EXAMPLE: Construct a discrete probability distribution for the number of heads when three coins are tossed. SOLUTION: Recall that the sample space for tossing three coins is TTT, TTH, THT, HTT, HHT, HTH, THH, and HHH. CHAPTER 7 The Binomial Distribution 115 The outcomes can be arranged according to the number of heads, as shown. 0 heads TTT 1 head TTH, THT, HTT 2 heads THH, HTH, HHT 3 heads HHH Finally, the outcomes and corresponding probabilities can be written in a table, as shown. Outcome, x 0123 Probability, P(x) 1 8 3 8 3 8 1 8 The sum of the probabilities of a probability distribution must be 1. A discrete probability distribution can also be shown graphically by labeling the x axis with the values of the outcomes and letting the values on the y axis represent the probabilities for the outcomes. The graph for the discrete probability distribution of the number of heads occurring when three coins are tossed is shown in Figure 7-1. There are many kinds of discrete probability distributions; however, the distribution of the number of heads when three coins are tossed is a special kind of ... each trial 3/17 Binomial Distribution Notation for the Binomial: B = Binomial Probability Distribution Function X ~ B(n, p) Read this as "X is a random variable with a binomial distribution. "... replaced once 7/17 Binomial Distribution they are drawn (one person cannot be two captains) You want to see if the captains all play the same position State whether this is binomial or not and... Chapter Review A statistical experiment can be classified as a binomial experiment if the following conditions are met: 8/17 Binomial Distribution There are a fixed number of trials, n There are