...300 SECRETS 1. A life is a terrible thing to waste. So easy to beat yourself up over mistakes you've made. So many amongst us live in the past rather than loving the present and building a brilliant future. First of all, no one tries to fail or mess things up. Every one of us wakes up in the morning, walks out into the world and does the best we can do based on what we know and the skills we have. But even more importantly, every so-called "mistake' is actually a rich source of learning. An opportunity to build more awareness and understanding and gain precious experience. Just maybe what we could call failures are actually growth lessons in wolf's clothing. And just maybe the person who experiences the most, wins. 2. A world-class company puts systems in place to ensure consistency of results. If you want to get something done and if you want to see consistent results, build a system around it. Celebrate the previous days wins and then rededicate to work for the mission. Systems‛ thinking builds structures into your life so that your best practices actually get integrated into your life. Systems allow you to live in a proactive rather than in a reactive way. And having a bunch of systems in place to keep you at your best doesn't mean that your life will be overly structured and full of stress Because nothing deprives a human being of happiness as much as seeing a life being wasted. 3. ABC. Always Be Connecting with everybody, everything around you. The best leaders build strong...
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...Kiara S. Randolph about 518 words 12197 Raccoon Rd Manning, SC 29102 678-314-2717 simeonrandolph@gmail.com don’t tell me i’m not By Kiara S. Randolph Seems like all I’ve ever heard is what I couldn’t and wouldn’t be... Just because I’m 5’5 and would rather stay in and read; then play outside don’t tell me I would never make the team. Just because I’m slow to speak and in crowds I tend to blend; rather than be the life of the party don’t tell me that I don’t deserve to be heard. My mother a janitor and my father a mechanic; hardworking but doesn’t come from money don’t tell me I can’t be a doctor. The youngest of three; my sister a model, my brother a star of tomorrow don’t tell me my future is anything less. I struggle with my weight; my mom trades my burgers for grapes. I walk down the hall, they point fingers, laugh at my temporary state, just because I’m 15 and overweight don’t tell me I could never be Miss USA. When I speak I stutter, one word becomes an echo of many. People poke fun call me retarded, but feelings I’ve got plenty. Just because I have a tough time being heard don’t tell me I can’t be a public speaker. The alarm rings, my face hits the floor before my feet. Soccer? More like the ball kicks me. Make the table for dinner? Forget it! Goofy names I answer to, but makes me feel less than, just because I lose everything I seem to grab don’t tell me that I’ll never have. Michael Jordan, Usain Bolt, Jackie Robinson; is that all you...
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...AS History: Enquiry Paper Guidance Question (a) – The Comparison. In question (a) the focus is on the direct comparison of two sources. Without explicit comparison candidates will not get above Band IV. A substantial number of candidates still adopt a sequential approach, and others limit themselves to a low Band III by confining their comparisons to a brief conclusion after a sequential analysis of the two Sources. A continuously comparative approach is required. Candidates should, however, not assume that a comparison is established simply by the introduction of comparative words and phrases such as ‘whereas’, ‘on the other hand’, ‘by contrast’, or by setting points from the Sources alongside each other. Similarity or difference of content has to be demonstrated in relation to a point which is genuinely comparable, either because both Sources refer to it or because one draws attention to it but the other ignores it. Likewise comparison of qualities other than content requires assessment of the same qualities in both Sources. Another common weakness is a failure to realise that comparisons are only relevant if they relate to the issue raised in the question. * Sequencing is a major problem. There is a reluctance to select issues and themes from the two Sources and build the comparison around these. Many candidates, often able, prefer paraphrase. Two separate accounts are provided with perhaps a final paragraph making a few belated comparisons. * Not focusing...
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... 01. Your knowledge of chemicals and their hazards, (i) Very Good (iv) Poor 02. (ii) Good (v) Very Poor Your interest in using PPE, (i) Very Good (ii) Good (iv) Poor 03. (iii) Average (iii) Average (v) Very Poor Your interest to get a help of superiors when you encounted problems in using chemicals, (i) Very Good (iv) Poor 04. (ii) Good (v) Very Poor Your awareness of how to act in an emergency situation, (i) Very Good (ii) Good (iv) Poor 05. (v) Very Poor (iii) Average Neatness and tidiness of your working environment, (i) Very Good (ii) Good (iv) Poor 06. (iii) Average (iii) Average (v) Very Poor Your understanding on warning symbols, and product warning labels, (i) Very Good (ii) Good (iv) Poor (v) Very Poor iii (iii) Average 07. Your knowledge in methods to follow in storing chemicals, (i) Very Good (iv) Poor 08. (ii) Good (v) Very Poor Your ability to perform your duties efficiently and effectively as planned, (i) Very Good (ii) Good (iv) Poor 09. (v) Very Poor (ii) No Your satisfaction on the methods follow in disposal in chemical waste, (i) Very Good (ii) Good (iv) Poor 11. (v) Very Poor (ii) Good (iv) Poor (v) Very Poor (ii) Good (iv) Poor (v) Very Poor (iii) Average Your concern of your health and safety in performing duties, (i) Very Good (ii) Good (iv) Poor 14. (iii) Average Amount...
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...The Begging of Broadcast Television - Broadcast Television on a national level began on July 1, 1941, - 1947 had only 60,000 TV sets in the USA, in bars, malls, and upper class homes - In 1951, over 10 million TV sets existed in the USA, virtually owned by everyone Technical Considerations - RCA-NBC pushed for black and white broadcasting in VHF (Very High Frequency) - CBS pushed to establish colour broadcasting in UHF (Ultra High Frequency) - RCA-NBC & VHF prevailed, surpassing its competitor, but could only appear on a limited amount of screens simultaneously - This caused them to stop selling licenses from 1948 – 1952, until the problem was fixed, and more stations were able to operate in different towns & cities. Political Considerations - Non-profit and educational broadcasting suffered in 1934, when the Wagner-Hatfield Bill was rejected by congress - The Bill was made so that 25% of broadcasting frequencies would be reserved for educational and non-profit broadcasting. Economic Considerations - Creating a national broadcasting system was too expensive to support non-profit & educational specials - Thus, already established commercial radio networks undertook financing of the development of broadcasting television in the US. - Television became a means of selling products with some entertainment to fill out the time between advertisements Analysis on Lipsitz and Haralovitch Readings: Lipsitz: “The...
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...unpredictable and chancy in case of an individual is predictable and uniform in the case of a large group. * This law forms the basis for the expectation of probable-loss upon which insurance premium rates are computed. Also called law of averages. Law of Large Numbers Observe a random variable X very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μ X of X. 4.slide ; Law of Large Numbers for Discrete Random Variables * The Law of Large Numbers, which is a theorem proved about the mathematical model of probability, shows that this model is consistent with the frequency interpretation of probability. 5.slide ; Chebyshev Inequality * To discuss the Law of Large Numbers, we first need an important inequality called the Chebyshev Inequality. * Chebyshev’s Inequality is a formula in probability theory that relates to the distribution of numbers in a set. * This formula is able to prove with little provided information the probability of outliers existing at a certain interval. 6.slide * Given X is a random variable, A stands for the mean of the set, K is the number of standard deviations, and Y is the value of the standard deviation, the formula reads as follows: *...
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...the monthly total costs? L + U + F = L + 3,995 + 11 x M 2 Gentle Lentil’s Monthly Earnings,cont. What are the monthly revenues? R = monthly revenues P = price of meal R = PxM What are the monthly earnings? X = monthly earnings = revenues – costs = P x M – ( L + 3,995 + 11 x M ) = (P – 11 ) x M – L – 3,995 Which of these quantities are random variables? P M L X = = = = price of prix fixe meal number of meals sold labor cost monthly earnings 3 (X is a function of random variables, so it is a random variable) Assumptions Regarding the Behavior of the Random Variables M P = number of meals sold per month We assume that M obeys a Normal distribution with µ = 3,000 and σ = 1,000 = price of the prix fixe meal We assume that P obeys the following discrete probability distribution Scenario Very healthy market Healthy market Not so healthy market Unhealthy market Price of Prix Fixe Meal $20.00 $18.50 $16.50 $15.00 Probability 0.25 0.35 0.30 0.10 L = labor costs per month We assume that L obeys a uniform distribution with a minimum of $5,040 and maximum of $6,860 4 The Behavior of the Random Variables, cont. X = earnings per month We do not know the distribution of X . We assume, however, that X = (P – 11 ) x M – L – 3,995 Always ask the following questions in any management analysis: • •...
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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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...number of times that a copier machine would break down over a year’s time, the average repair time days, and lastly the estimated loss of revenue that occurred when the machine broke down each time. The owners of the company needed this information to make a decision on whether or not to purchase a backup copier. I decided to start with the table on page 679, which identified the probability of the days that it took the copier to get fixed each time that it broke down. I calculated the cumulative probability before beginning my simulation. I figured that in a year’s time with a max of six weeks between breakdowns according to the information given, that the copier would break down approximately 15 times. In Excel, I created fifteen random numbers (RN1) based upon my cumulative probability and probability distribution given. After which, I determined an average number of repair days for each break down which calculated to be about 2 days. The second step taken to begin this simulation was to determine the frequency of how often the copier would break down. The probability given was based upon speaking with staff members from the college of business and notating that the probability of the break downs increased the longer the copier went without breaking down. In looking at the visual provided on page 679, I was able to use the formula y=mx+b in order to find the probability for each week, given at week six, 0.33. I first found the slope using rise over run 0.33/6 which...
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...machine in the event that it broke down. As discovered, the average time for repair was between one and four days. In order to calculate the average, a probability distribution was developed using Microsoft Excel. From there, the cumulative probability was obtained by adding the probability, P(x), from the previously itemized probabilities where the cumulative summation of a probability is always equal to one (1) or 100%. A random number formula, =RAND(), was plugged into the Microsoft Excel desired cell, in this situation, (H4), which generated a random range of numbers that are greater than or equal to zero and less than one. The interim time between breakdowns were achieved simply by soliciting the experience several staff members in the college of business who were familiar with frequency of the copier’s inconsistent behavior. It was estimated that the time between breakdowns was probably between zero and six weeks. Using the continuous probability distribution formula, x=6√r1, where six is the maximum number of weeks in this study and r1 is the random number. The amount of breakdowns were achieved by attaining the result of the cumulative time after determining that the number of breakdowns needed to assess the case study of approximately...
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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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...DISTRIBUTION IS UNIPARAMETRIC ONE. 4. THE CONDITIONS FOR THE POISSION MODEL ARE : • THE PROBABILIY OF SUCCESS IN A VERY SMALL INTERAVAL IS CONSTANT. • THE PROBABILITY OF HAVING MORE THAN ONE SUCCESS IN THE ABOVE REFERRED SMALL TIME INTERVAL IS VERY LOW. • THE PROBABILITY OF SUCCESS IS INDEPENDENT OF t FOR THE TIME INTERVAL(t ,t+dt) . 5. Expected Value or Mathematical Expectation of a random variable may be defined as the sum of the products of the different values taken by the random variable and the corresponding probabilities. Hence if a random variable X takes n values X1, X2,………… Xn with corresponding probabilities p1, p2, p3, ………. pn, then expected value of X is given by µ = E (x) = Σ pi xi . Expected value of X2 is given by E ( X2 ) = Σ pi xi2 Variance of x, is given by σ2 = E(x- µ)2 = E(x2)- µ2 Expectation of a constant k is k i.e. E(k) = k fo any constant k. Expectation of sum of two random variables is the sum of their expectations i.e. E(x +y) = E(x) + E(y) for any two random variable x and y Expectation of the product of a constant and a random variable is the product of the constant and the expectation of the random variable. i.e. E(k x) = k.E(x) for any constant k Expectation of the product of two random variable is the product of the i.e. E(xy) = E(x) . E(y) Whenever x and y are independent....
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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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...46 Probability, Random Variables and Expectations Exercises Exercise 1.1. Prove that E [a + b X ] = a + b E [X ] when X is a continuous random variable. Exercise 1.2. Prove that V [a + b X ] = b 2 V [X ] when X is a continuous random variable. Exercise 1.3. Prove that Cov [a + b X , c + d Y ] = b d Cov [X , Y ] when X and Y are a continuous random variables. Exercise 1.4. Prove that V [a + b X + c Y ] = b 2 V [X ] + c 2 V [Y ] + 2b c Cov [X , Y ] when X and Y are a continuous random variables. ¯ Exercise 1.5. Suppose {X i } is an sequence of random variables. Show that V X = V 2 2 σ where σ is V [X 1 ]. time. 1.4 Expectations and Moments 47 i. Assuming 99% of trades are legitimate, what is the probability that a detected trade is rogue? Explain the intuition behind this result. ii. Is this a useful test? Why or why not? Exercise 1.13. You corporate finance professor uses a few jokes to add levity to his lectures. He is also very busy, and so forgets week to week which jokes were used. i. Assuming he has 12 jokes, what is the probability of 1 repeat across 2 consecutive weeks? ii. What is the probability of hearing 2 of the same jokes in consecutive weeks? iii. What is the probability that all 3 jokes are the same? iv. Assuming the term is 8 weeks long, and they your professor has 96 jokes, what is the probability that there is no repetition across the term? Note: he remembers the jokes he gives in a particular lecture, only forgets across...
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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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