Probability Discrete Event Simulation: Tutorial on Probability and Random Variables 1. A card is drawn from an ordinary deck of 52 playing cards. Find the probability that it is (a) an Ace, (b) a jack of hearts, (c) a three of clubs or a six of diamonds, (d) a heart, (e) any suit except hearts, (f) a ten of spade, (g) neither a four nor a club (1/3, 1/52, 1/26, 1/4, 3/4, 4/13, 9/13) 2. A ball is drawn at random from a box containing six red balls, 4 white balls and 5 blue balls. Determine
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Probability & Mathematical Statistics | “The frequency concept of Probability” | [Type the author name] | What is probability & Mathematical Statistics? It is the mathematical machinery necessary to answer questions about uncertain events. Where scientists, engineers and so forth need to make results and findings to these uncertain events precise... Random experiment “A random experiment is an experiment, trial, or observation that can be repeated numerous times under the
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Probability and odds are two basic statistic terms to describe the likeliness that an event will occur. In everyday conversation “probability” and “odds” are used interchangeably. If something has a high probability it always also has a high odds of happening. In reality, the Probability of something happening and the odds of something happening are two completely different ways of describing the chances. Simple probability of event A occurring is mathematically defined as: Odds are the ratio
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Quant Investments “It had not been a particularly good year for Quant Investments”, mused Alain over his pate de foie gras and champagne. It was lunchtime on Christmas Eve, and his three colleagues Belén, Carlos and Dawood had already set off on holiday to far-off, exotic locations. The four of them had worked as a close team of analysts for the past 15 months since graduating as MBAs, and Alain realised that their performances had not come up to expectations. Alain feared that all four may
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Probability review (week 2) 1 Bernoulli, Binomial, Poisson and normal distributions. In this excercise we deal with Bernoulli, binomial, Poisson and normal random variables (RVs). A Bernoulli RV X models experiments, such as a coin toss, where success happens with probability p and failure with probability 1 − p. Success is indicated by X = 1 and failure by X = 0. Therefore, the probability mass function (pmf) of X is P {X = 0} = 1 − p, P {X = 1} = p (1) A binomial random variable (RV)
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7.10.2015 г. 1 1. Experiment, Outcomes, and Sample space 2. Random Variables 3. Probability Distribution of a Discrete Random Variable 4. The Binomial Probability Distribution 5. The Hypergeometric Probability Distribution 6. The Poisson Probability Distribution 7. Continuous Random Variables 8. The Normal Distribution 9. The Normal Approximation to the Binomial Distribution 2 1 7.10.2015 г. An experiment is a process that, when performed, results in one and only one
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What are the two basic laws of probability? What are the differences between a discrete probability distribution and a continuous probability distribution? Provide at least one example of each type of probability distribution. The two basic laws of probability are adding mutually exclusive events and addition for events that are not mutually exclusive (Render, Stair & Hanna, 2008). The probability must be between zero and one for any event just as the sum must equal one of all the events. Therefore
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the following becomes true fTt=12ttxdx Integrating the above equation, we have; fTt=964t2 Varying the same in the interval2<x<4), we have fTt=12tt38xdx Integrating the equation and solving accordingly we get fTt=-3t264+34 Therefore, probability that a randomly chosen claim on this policy is processed in three hours or more; PrT>3=34(-3t264+34)dt Integrating the equation and solving accordingly we get; PrT>3=34-1-2764
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4 6 8 3 12 7 7 8 3 10 3 5 8 7 9 6 6 12 4 7 9 9 11 4 5 2 5 2 3 5 3 10 2 2 4 3 6 3 10 7 7 9 8 5 12 3. (22 pts) Find the experimental probability of rolling each sum. Fill out the following table: Sum of the dice Number of times each sum occurred Probability of occurrence for each sum out of your 108 total rolls (record your probabilities to three decimal places) 2 10 .092 3 13 .120 4 10 .092 5 11 .101 6 9 .083 7 19 .175 8 9 .083 9 9 .083 10 7 .064 11 2
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Probability- long run relative frequency. The proportion of times the outcome would occur in a very long series of repetitions Law of large numbers- the long run frequency of repeated events eventually produces the true relative frequency. This is called the empirical probability or objective probability. When we can’t repeat events the probability of an event is called subjective or personal probability. If A and B are disjoint, P(A or B)= P(A) + P(B) General addition rule- P(A or B) = P(A) +
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