handle Dependent Events Life is full of random events! You need to get a "feel" for them to be a smart and successful person. Independent Events Events can be "Independent"‚ meaning each event is not affected by any other events. Example: Tossing a coin. Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. The chance is simply 1-in-2‚ or 50%‚ just like ANY toss of the coin. So each toss is an Independent Event. Dependent Events But events can also
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The Role of Extinction in Evolution In contrast to the opposite phenomenon‚ speciation. This is surprising in view of the special importance Darwin attached to extinction‚ and because the number of species extinctions in the history of life is almost the same as the number of originations; present-day biodiversity is the result of a trivial surplus of originations‚ cumulated over millions of years. For an evolutionary biologist to ignore extinction is probably as foolhardy as for a demographer
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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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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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certain tone followed by an event can train a certain response from a dog or human‚ for example if you ring a bell then feed your dog the dog will associate the bell with the food. If a special someone always wears a certain smell when they are around you‚ and you happen to smell that scent you will become excited. This type of learning is called acquisition. Acquisition is the initial learning. But as quick as you learn a trigger signal you can also not associate it with an event. If you normally ring
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time scale of our earth and solar system‚ it is difficult to comprehend its scale at the surface. A mass extinction is classified as a massive dying of animal species in a short geologic window. In the above analogy that would mean having anywhere from 70% to 90% of creature species die in a fraction of a second. Mass extinctions are driven by a compounding of events. For example‚ the extinction that defined the beginning of the Triassic was called quite literally: The Great Dying. During the Great
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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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