# Probability theory

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There is no inventor, known contributors, and early uses. For instance, one can find the true and false values for a computer program. P(A|B) = P (A (B) / P (B) is the conditional probability representation. In additional, truth tables and probability are today uses. Bayes Theorem is the final concept in statistics, which is defined as the description of the probability of events based on related conditions. Thomas Bayes developed P (A|B) = P (B|A) (P (A) / P (B) where Pierre-Simon Laplace further the Bayes theorem formula and Sir Harold Jeffreys defined the Bayes Theorem as the theory probability. There are no early uses and is used for probability, odds, conditional probability, etc. For example, the question, what will be the chance of getting gestational diabetes with your first child, will be the practical example. According to Hilaire Belloc, “Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death” (Statistics Quotes,…

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Transaction utility theory Jha-Dang (2004) explains that the concept of transaction utility state that the total utility derived from a purchase comprised of acquisition utility and transaction utility. He describes acquisition utility as the expected utility gained from acquiring the product (i.e. benefits of the product) compared to the cost of paying for it (i.e. the price of the product); while transaction utility is the difference between the internal reference price and purchase price of…

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1 Introduction Many praises have been used to describe Black-Scholes’ pricing theory, which is the most successful and widely used in the application. Although the elegant Black-Scholes’ theory is, there is an absolute disadvantage(Heston 1993). The strong assumption of constant volatility cannot express high peak and flat tail character of derivatives, and the relative between the spot return and the variance. Therefore, there are several theories try to extend and modify the original…

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The Haybaler Problem In The Haybaler Problem we were trying to see how much each bale of hay weighed, and if there is more than one answer. There were 5 bales of hay in total, and when put together they would equal 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91. So I decided to start doing guess and check like this: A+B=80 and then substituting numbers like 39+41=80. I did it like this because I needed to come up with at least one number to start off. I tried different numbers like 39, 38, 40, and…

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product. Hence, the first partial product is 110111100. All of the partial products will have nine bits length. Next, the second partial product is determined by next three bits i.e. multiply by 2. Multiply by 2 means the multiplicand value has to shift left one bit. So, the second partial product is 001000100. Similarly the third partial product has to multiply by 1. So, the third partial product is the multiplicand value namely 000100010. The fourth partial product is determined by next three…

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Axiom of choice was formulated by Zermelo in 1904 and is known as Zermelo’s axiom of choice. This axiom stated that we can choose a member from each set in a collection of nonempty disjoint sets, C (Schechter, 2009). Additionally, according to Janes (2008), there exists a set X which consisting of one element taken from each set belonging to Y given that any nonempty set Y members are pairwise disjoint sets. Taking a role as a basic assumption used in many parts of mathematics as stated by…

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/* 1 */ - This variable is equal to a constructor function called Winston. A constructor function is a function that is called everytime a new instance of this variable is created The parameters of this specific function are nickname, age, x, and y. /* 2 */ - In this line, this. refers to the current object instance which in this case is nickname. It is basically saying that the nickname property of this is equal to whatever is passed in the constructor function itself. This object is…

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test different ranking algorithms and will provide results so we can show how the Information Gain Ranking filter will outperform the other algorithms for attribute selection in our data set. The Information Gain Ranking filter is an entropy based filter that helps us to identify the gain of the attributes. For example an Entropy for i classes can be defined as: Entropy is very often employed, generally in the information theory measure. It is the foundation of the Information Gain Attribute…

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As we model this Markov process, we observe the state-dependent output, yet initially we are not able to note any of the states. Each state has a unique probability distribution over each possible output. Thus, information about the sequence of states through which the model makes its way can be obtained from the sequence of outputs generated, while the rest of the model remains hidden. The algorithm tracks a stochastic process through its states by using a recursive method that is optimal in…

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For the application of Hopf’s bifurcation theory to the system (29) (see [Marsden J.E., M. Mckracken, 1976]), it is required to satisfy the following transversality condition (34) Substituting , and into (31), and calculating the derivatives with respect to , we obtain (35) where Since , we have , and . Hence there is a Hopf bifurcation at . We have the following result: Theorem 13. Suppose holds. Then the system (29) undergoes a Hopf…

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