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    experiment. (b) Describe a possible relevant choice for the field F . (c) Define two events that are mutually exclusive. (d) Define two events that have a nonempty intersection. Problem 3 A photon counter connected to the output of a fiber detects the number of photons‚ {Ni ‚ i 1}‚ received for successive pulses generated by a laser connected to the input of the fiber. Specify which one of the following sequences of events‚ {Ek ‚ k 1} is increasing‚ decreasing or none. Very briefly explain why. (a) Ek

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    activity is required to think of every possible cost would be happened in the process of delivering an event. Budgeting is to deal with the financial management applying the financial tools and techniques. It is significantly to make decision on each segment‚ such as staff‚ venue‚ to ensure the resource is efficiency to use. 2. Briefly define three of the following concepts in the context of event design/theming - balance‚ emphasis‚ design‚ harmony‚ rhythm and proportion. Proportion is a connection

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    Probability Theory

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    I. Probability Theory * A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs‚ but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. * The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation

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    department‚ USC‚ Fall 2014 Instructor: Prof. Salman Avestimehr Homework 1 Solutions 1. (Axioms of Probability) Prove the union bound: n P [∪n Ak ] ≤ k=1 P [Aj ]. j=1 The union bound is useful because it does not require that the events Aj be independent or disjoint. Problem 1 Solution We prove this part by induction‚ for k = 2 we have P (A1 ∪ A2 ) = P (A1 ) + P (A2 ) − P (A1 ∩ A2 ) ≤ P (A1 ) + P (A2 ) (1) Now‚ assume that the statement is true for k = n n P (A1 ∪ A2

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    Assignment12 1

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    APStatistics Statistics Assignment 12: Rules of Probability Directions: Complete the assignment on your own paper. Clearly label each answer. (34 points) 1. You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. (8 points) a. Create a sample space. {1‚ 2‚ 3‚ 4‚ 5‚ 6} b. P (getting a 1 on the first die or getting a 6 on the second die) 1/6+1/6= .333 c. P (getting a 3 on the second die given that

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    probability is the probability that an event will occur given that another has already occurred. If A and B are two events‚ then the conditional probability A given B is written as P ( A | B ) and read as “the probability of A given that B has already occurred.” We are to calculate the probability of the intersection of the events F and G. P(F and G) = P(F) P(G |F) P(F) = 13/40 P(G |F) = 4/13 P(F and G) = P(F) P(G |F) = (13/40)(4/13) = .100 Union of Events P(A or B) = P(A) + P(B) – P(A and

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    Probability Theory

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    GOALS When you have completed this chapter‚ you will be able to ONEDefine probability. TWO Describe the classical‚ empirical‚ and subjective approaches to probability. THREEUnderstand the terms experiment‚ event‚ outcome‚ permutation‚ and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and compute probabilities. SEVEN Calculate a probability using Bayes

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    Theory of Probability

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    Enterprise Solution Division Random Process In a random process we know that what outcomes or events could happen; but we do not know which particular outcome or event will happen. For example tossing of coin‚ rolling of dice‚ roulette wheel‚ changes in valuation in shares‚ demand of particular product etc. Probability It is the numeric value representing the chance‚ likelihood‚ or possibility a particular event will occur     It is measured as the fraction between 0 & 1 (or 0% &100%) Probability

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    a particular event will happen if something is done repeatedly‚ (596 Webster’s Dictionary). You cannot determine any events that will happen in the future‚ because there is always a chance that something odd will happen‚ (Linn 39-40). Probability originally started for the purpose and attempt to analyze games of chance. Probability is also used in determining the outcomes of an experiment. Sample space is the collection of all results. Probability is a way to assign every event a value between

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    Probablity

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    the likelihood of an event happening. Directly or indirectly‚ probability plays a role in all activities. Probability is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability‚ the more likely the event is to happen‚ or‚ in a longer series of samples‚ the greater the number of times such event is expected to happen

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