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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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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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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What would you do if there was a violent car crash in front of you? What if someone was drowning or being attacked? Would you risk your safety or well-being for others? While at a block party last Fourth of July‚ a dangerous accident made me realize how brave I could be. I live on a cul-de-sac with a roommate‚ Chris. Chris and I were invited‚ by our neighbors‚ to a block party this past Fourth of July. They were going to have plenty of food‚ drinks‚ fireworks‚ and games for kids and adults alike
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Vision for the Plan: As a teacher‚ I want to be professional and a positive role model to my students. I want to have a good and supportive environment in my classroom so that it allows my students to have good opportunities to succeed. I will keep motivate my students to be better in their work and it is my job to make sure that each students learn something. Therefore‚ I plan to use positive reinforcement in the classroom and praise any positive behavior in the classroom. I will use the classroom
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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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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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