...Norm Violation The norm violation I chose was to take groceries out of peoples cart at the grocery store. I set a time limit and did this for forty-five minutes to random people at the store. I chose this norm because it is close to home and I didn’t want to do something too risky due to my anxiety, so this was a bit easier than something like in the school, or at work. This norm violation was fun as well as a little scary, and everyone needs that once in a while. The setting I chose was at Dillons, I shop here quite a bit so it wasn’t too far out of my comfort zone. I chose this as a social setting as well because since I shop there so much I know that I don’t really see many people I know. I only see people I know at the Dillons on 30th...
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...CHAPTER 6 RANDOM VARIABLES PART 1 – Discrete and Continuous Random Variables OBJECTIVE(S): • Students will learn how to use a probability distribution to answer questions about possible values of a random variable. • Students will learn how to calculate the mean and standard deviation of a discrete random variable. • Students will learn how to interpret the mean and standard deviation of a random variable. Random Variable – Probability Distribution - Discrete Random Variable - The probabilities of a probability distribution must satisfy two requirements: a. b. Mean (expected value) of a discrete random variable [pic]= E(X) = = 1. In 2010, there were 1319 games played in the National Hockey League’s regular season. Imagine selecting one of these games at random and then randomly selecting one of the two teams that played in the game. Define the random variable X = number of goals scored by a randomly selected team in a randomly selected game. The table below gives the probability distribution of X: Goals: 0 1 2 3 4 5 6 7 8 9 Probability: 0.061 0.154 0.228 0.229 0.173 0.094 0.041 0.015 0.004 0.001 a. Show that the probability distribution for X is legitimate. b. Make a histogram of the probability distribution. Describe what you see. 0.25 0.20 0.15 0.10 ...
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...can begin to use probabilistic ideas in statistical inference and modelling, and the study of stochastic processes. Probability axioms. Conditional probability and independence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting distributions. The syllabus is as follows: 1. Basic notions of probability. Sample spaces, events, relative frequency, probability axioms. 2. Finite sample spaces. Methods of enumeration. Combinatorial probability. 3. Conditional probability. Theorem of total probability. Bayes theorem. 4. Independence of two events. Mutual independence of n events. Sampling with and without replacement. 5. Random variables. Univariate distributions - discrete, continuous, mixed. Standard distributions - hypergeometric, binomial, geometric, Poisson, uniform, normal, exponential. Probability mass function, density function, distribution function. Probabilities of events in terms of random variables. 6. Transformations of a single random variable. Mean, variance, median, quantiles. 7. Joint distribution of two random variables. Marginal and conditional distributions. Independence. iii iv 8. Covariance, correlation. Means and variances of linear functions of random variables. 9. Limiting distributions in the Binomial case. These course notes explain the naterial in the syllabus. They have been “fieldtested” on the class of 2000. Many of the examples...
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...chosen randomly, what is the probability that he or she is taking exactly one language class? (c) If 2 students are chosen randomly without replacement, what is the probability that at least one is taking a language class? 4. A CEO wants to decide how much to invest on a project. If the firm invest x, then the probability of success is 1 − e−2x . If the project succeeds, then the firm earns 1, and if not, nothing. Let Y be the earning from the project. The profit function of the firm is given by π(Y |x) = Y − x. (a) Derive the expected profit function, Eπ(Y |x). (b) Suppose that the firm is risk neutral, and therefore wants to maximize the expected profit. How much should they invest? 5. A researcher wants to know how many people have experience in gambling. However, people usually do not answer frankly to such a subtle question. So, she devises the following procedure. First, the respondent tosses a fair coin secretly....
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...mathematical expression which gives the sum of four rolls of a die. To do this, we could let Xi , i = 1, 2, 3, 4, represent the values of the outcomes of the four rolls, and then we could write the expression X 1 + X 2 + X 3 + X4 for the sum of the four rolls. The Xi ’s are called random variables. A random variable is simply an expression whose value is the outcome of a particular experiment. Just as in the case of other types of variables in mathematics, random variables can take on different values. Let X be the random variable which represents the roll of one die. We shall assign probabilities to the possible outcomes of this experiment. We do this by assigning to each outcome ωj a nonnegative number m(ωj ) in such a way that m(ω1 ) + m(ω2 ) + · · · + m(ω6 ) = 1 . The function m(ωj ) is called the distribution function of the random variable X. For the case of the roll of the die we would assign equal probabilities or probabilities 1/6 to each of the outcomes. With this assignment of probabilities, one could write P (X ≤ 4) = 1 2 3 2 CHAPTER 1. DISCRETE PROBABILITY DISTRIBUTIONS to mean that the probability is 2/3 that a roll of a die will have a value which does not exceed 4. Let Y be the random variable which represents the toss of a coin. In this case, there are two possible outcomes, which we can label as H and T. Unless we have reason...
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...STAT200 final exam 2016 Click Link Below To Buy: http://hwcampus.com/shop/stat200-final-exam-2016/ On Multiple Choice questions, please explain and/or show your work as necessary. Other questions please show your work as well. _____1. Ten different senators are randomly selected without replacement, and the number of terms that they have served are recorded. Does this constitute a binomial distribution? Select an answer, and then state why. a. No b. Yes Why: _____2. Which of the following pairs are NOT independent events? a. Flipping a coin and getting a head, then flipping a coin and getting a tail b. Throwing a die and getting a 6, then throwing a die and getting a 5 c. Selecting a red marble from a bag, returning the marble to the bag, then selecting a blue marble d. Drawing a spade from a set of poker cards, setting the card aside, then selecting a diamond from the set of poker cards e. All of the above are independent events _____3. Exam scores from a previous STATS 200 course are normally distributed with a mean of 74 and standard deviation of 2.65. Approximately 95% of its area is within: a. One standard deviation of the mean b. Two standard deviations of the mean c. Three standard deviations of the mean d. Depends on the number of outliers e. Must determine the z-scores first to determine the area _____4. You had no chance to study for the final exam and had to guess for each question. The instructor gave you three choices for the...
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...1.10 Sampling Distributions The main objective of most statistical inference is to draw conclusion about the population parameters based on samples studies that is quite small in comparison to the size of the population. In order that conclusion of sampling theory and statistical inference valid, samples must be chosen so as to the representation of a population. For example, Television executives want to know the proportion of television viewers who watch that network’s program. Particularly determining the proportions that are watching certain programs is impractical and prohibitively expensive. One possible alternative method can be providing approximation by observing what a sample of 1,000 television viewer’s watch. Thus they estimate the population proportion by calculating the sample proportion. Similarly, the field of quality control illustrates yet another reason for sampling. In order to ensure that a production process is operating properly, the operations manager needs to know the proportion of defective units that are being produced. If the quality-control technician must destroy the unit in order to determine whether or not it is defective, there is no alternative to sampling: a complete inspection of the population would destroy the entire output of the production process. We know that the sample proportion of television viewers or of defective items is probably not exactly equal to the population proportion we want it to estimate. Nonetheless, the sample statistic...
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...Finding out the cause of sales-stickiness Of Times of India published Bengali news daily Ei Samay By Saswata Biswas June, 2015 Finding out the cause of sales-stickiness Of Times of India published Bengali news daily Ei Samay By Saswata Biswas Under the guidance of Shri Rupak Sengupta Dr. Soma Arora AGM,RMD Assistant Professor Times Group IMT, Ghaziabad June, 2015 Certificate of Approval The following Summer Project Report titled " Finding out the cause of sales-stickiness of Times of India published Bengali news daily Ei Samay " is hereby approved as a certified study in management carried out and presented in a manner satisfactory to warrant its acceptance as a prerequisite for the award of Post-Graduate Diploma in Management for which it has been submitted. It is understood that by this approval the undersigned do not necessarily endorse or approve any statement made, opinion expressed or conclusion drawn therein but approve the Summer Project Report only for the purpose it is submitted. Summer Project Report Examination Committee for evaluation of Summer Project Report Name Signature 1. Faculty Examiner _______________________ ___________________ 2. PG Summer Project Co-coordinator _______________________ ___________________ Certificate from Summer Project Guides This is to certify that Mr. /Ms. Saswata Biswas, a student of the Post-Graduate Diploma in Management, has worked...
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... mean (average) Variance 2 probability density function 1 x 2 1 exp f x 2 2 cumulative density function 1 t 2 1 F x dt exp 2 2 Standard Normal Density X ~ N 0,1 probability density function n x cumulative density function x N x 1 1 exp x 2 2 2 x important result: standardization 1 exp t 2 dt 2 2 1 if X~N , 2 and Z= then Z~N 0,1 X- 1 Mathematical Expectation: Given a random variable X and its pdf f x we define the expectation of the function g X to be the integral E g X g x f x dx Note that g X is also a random variable The Moment Generating Function (MGF) The MGF of a random variable X is a function of t denoted by M X t E e xt which is an expectation MGF of normal If X ~ N , 2 1 x 1 Xt xt Then M X t E e e e 2 2 Lognormal Distribution: 2 1 t 2t 2 dx e 2 Y has the lognormal distribution with parameters , 2 if: its logarithm is normally distributed X log e Y ~ N , 2 . This in turn means that Y e X 2 The cumulative density function of Y is log e y FY y Pr Y y N x 12 1 2t where N x ...
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...at least 6 free throws? A) 0.2936 B) 0.3355 C) 0.7969 D) 0.1678 D) 0.1468 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box. A sample of boxes results in the following table. 14 15 16 17 Weight in Ounces Probability 0.10 0.30 0.40 0.20 5) What is the mean weight of the sample of cereal boxes? A) 16.0 B) 15.7 C) 15.5 D) 16.5 D) 1.25 6) What is the standard deviation of the weight of cereal in the boxes? A) 1.19 B) 0.90 C) 0.81 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In an office of 18 people, there are 7 men and 11 women. A sub-committee of four people will be formed from this group. 7) What is the probability that the sub-committee contains two men and two women? A) 0.261 B) 0.377 C) 0.755 8) How many different ways can you select four people from a group of 18? A) 1584 B) 3280 C) 1386 D) 0.522 D) 3060 THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING...
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...Kellogg Mathematical Methods for Management Decisions Page 1 of 37 DECS – 433 Excel Functions and Tools DECS - 433 requires knowledge of various Excel functions and tools. This document attempts to explain and summarize your basic responsibilities in this regard. The information is presented in the following general categories: • Basic Excel Functions SUM PRODUCT SUMPRODUCT • MAX MIN Excel Functions Commonly used in Simulation RAND RANDBETWEEN IF IF(RAND( ) … ) IF( … IF( … )) IF(AND … ) IF(OR … ) COUNTIF SUMIF LOOKUP LOOKUP(RAND( ) … ) • Excel Functions Commonly used in Sampling AVERAGE VARP VAR STDEVP STDEV COVAR CORREL • Excel Functions Relating to Binomial Distributions FACT COMBIN BINOMDIST CRITBINOM CRITBINOM(… RAND( )) • Excel Functions Relating to Normal Distributions and T-Distributions NORMDIST NORMSDIST NORMINV NORMSINV NORMINV(RAND( ) … ) TDIST TINV • Useful Excel Tools Solver Data Tables Page 2 of 37 Basic Excel Functions • SUM( … ) The SUM function adds up a range of cells or specific numbers. One specifies the range or specific numbers within the parentheses. Example: 1 2 3 4 5 6 7 A 3 -8 15 6 12 28 B C Here we are adding specific numbers instead of referencing a range of cells. The formula underlying cell C7 is: = SUM(2, 4, 6) 12 Here we are adding cells A1 through A5. The formula underlying cell A7 is: =SUM(A1:A5) • PRODUCT( … ) The PRODUCT function multiplies ranges of cells or specific numbers. One specifies...
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...CHAPTER 1 : INTRODUCTION 1.1. BACKGROUND OF STUDY Life at the turn of the 21st century are exceptionally testing and not the us effectively we anticipated. Besides, the monetary emergency that is hitting the world these days is no special case for Malaysia likewise influences somewhat by ordinary life in life. As an aftereffect of this, of numerous who wander into the business to oblige the minimal present as a consequence of the present downturn now including understudies. This study is to see the effect of the college understudy working low maintenance on the execution of learning. The purpose of this study was to examine the work while the impression towards academic achievements. Percentage shows between 55% to 80% of students will work while learning (Miller, 1997; King, 1998). This high percentage is also causing some researchers to believe that the students who will work towards the achievement of academic decline (Steinberg, Dornbusch, & Fegley 1993). At the same time also, there are a discovered that work while learning provides a positive impact if they follow the correct percentage (In & Hoyt, 1981). Inquiry about "impression of working part time on academic Achievement" is mixed. Along these lines, the study will endeavour to give more proof of a much clearer and point by point to comprehend the impression of working low maintenance towards scholastic accomplishments in North Malaysia College understudies particularly. 1.2. STATEMENTS OF PROBLEM...
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...often as 4. This view, where randomness simply refers to situations where the certainty of the outcome is at issue, applies to concepts of chance, probability, and information entropy. In these situations, randomness implies a measure of uncertainty, and notions of haphazardness are irrelevant. The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory. Randomness is often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science.[2] Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, if we have a bowl of 100 marbles with 10 red (and any red marble is...
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...9. SAMPLING AND STATISTICAL INFERENCE We often need to know something about a large population. Eg: What is the average number of hours per week devoted to online social networking for all US residents? It’s often infeasible to examine the entire population. Instead, choose a small random sample and use the methods of statistical inference to draw conclusions about the population. But how can any small sample be completely representative? We can’t act as if statistics based on small samples are exactly representative of the entire population. Why not just use the sample mean x in place of μ? For example, suppose that the average hours for 100 randomlyselected US residents was x = 6.34. Can we conclude that the average hours for all US residents (μ) is 6.34? Can we conclude that μ > 6? Fortunately, we can use probability theory to understand how the process of taking a random sample will blur the information in a population. But first, we need to understand why and how the information is blurred. Sampling Variability Although the average social networking hours for all US residents is a fixed number, the average of a sample of 100 residents depends on precisely which sample is taken. In other words, the sample mean is subject to “sampling variability”. The problem is that by reporting x alone, we don’t take account of the variability caused by the sampling procedure. If we had polled different residents, we might have gotten a different average social networking hours. In general...
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...Spartans lead the FBS in time of possession (34:56 per game).(SpartyOn.com) In Michigan, from 2009 to 2013 there were 88.9 percent of people age of 25 above have education of high school graduate or higher which is higher than United State average of 86.0 percent, and also have 25.9 percent people have Bachelor’s degree or higher. In addition, Michigan has an average salary of jobs of $58,000. (Census.gov) Where these numbers came from? It is Statistics. “People cannot make research without statistics and analysis.”(Zeleke) Statistics is important and critical, it can solve for society problem. Nowadays, we have a lot of technological advancement, mobile technology and data in our daily life. The world becomes more and more complex. We need people to be proficient to understand all information out there. How do we process? What is important? How do we analyze the information and make the right decision? Now, there are lots of problem that we are facing: human, race, climate change, economics hardships, and political instability etc. For solving these problems, we need statistics and modeling. Statistics become more and more important; it is not only for statistician but also for everyone. Statistics not only help us organize the complicate data, but also help society. In other words, Statistics is also one of the strongest evidence; it can help people decide more things. Such as the research "Single statistic can strengthen public support for traffic safety laws." which given out...
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