Có 40+ tài liệu thuộc chủ đề "kinh tế ứng dụng"
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(x m ) is divergent but it does not diverge to. lim sup x m = x lim sup x m = y and lim inf x m = x lim sup x m. and lim inf x m = x x 1. lim sup f (x). lim inf f (x). f is upper semicontinuous but not lower semicontinuous at...
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Take any x 1 ∈ S. Show that inf S. x m − a | for each m.. for all k, k , l ∈ N . for all k ∈ N . Take any y ∈ (f (a), f (b. Show that f (sup S. A such that f(A. A for each A ∈ A . “butterfly hunting.” (If...
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(b) If one simulates a sufficiently large number of rolls, one should be able to conclude that the gamblers were correct.. Your simulation should result in about 25 days in a year having more than 60 percent boys in the large hospital and about 55 days in a year having more than 60 percent boys in the small hospital.. (a)...
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To do this, we could let X i , i represent the values of the outcomes of the four rolls, and then we could write the expression. for the sum of the four rolls. The function m(ω j ) is called the distribution function of the random variable X . For the case of the roll of the die we...
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The experiment consists of spinning the pointer and recording the label of the point at the tip of the pointer.. We will also assume that in this model, if E is an arc of the circle, and E is of length p, then the model will assign the probability p to E. Events are subsets of the unit square. Since...
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Consider an experiment that takes place in several stages and is such that the number of outcomes m at the nth stage is independent of the outcomes of the previous stages. From the tree diagram we see that the total number of choices is the product of the number of choices at each stage. Our menu example is an example...
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Suppose that before the election is held, A drops out of the race. We have just calculated the inverse probability that a particular urn was chosen, given the color of the ball. The reverse tree then displays all of the inverse, or Bayes, probabilities.. This aspect of the problem will be discussed in Sec- tion 4.3. Figure 4.3: The Monty...
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As is the case with all of the discrete probabil- ity distributions discussed in this chapter, this experiment can be simulated on a computer using the program GeneralSimulation. Thus, if the possible outcomes of the experiment are labelled ω 1 ω 2. ω n , then we use the above expression to represent the subscript of the output of the...
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Expected Value and Variance. 6.1 Expected Value of Discrete Random Variables. EXPECTED VALUE AND VARIANCE. Expected Value. The expected value E(X) is defined by. Thus, the expected value of X equals. EXPECTED VALUE 227. What is the expected value of the payment?. The reader is asked to show in Exercise 20 that the expected value of the payment is now...
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Sums of Independent Random Variables. 7.1 Sums of Discrete Random Variables. In this chapter we turn to the important question of determining the distribution of a sum of independent random variables in terms of the distributions of the individual constituents. In this section we consider only sums of discrete random variables, reserving the case of continuous random variables for the...
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Law of Large Numbers. 8.1 Law of Large Numbers for Discrete Random Variables. The Law of Large Numbers, which is a theorem proved about the mathematical model of probability, shows that this model is consistent with the frequency interpretation of probability. This theorem is sometimes called the law of averages. To discuss the Law of Large Numbers, we first need...
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We note that the maximum values of the distributions appeared near the ex- pected value np, which causes their spike graphs to drift off to the right as n in- creased. Now the maximum values of the distributions will always be near 0.. We make the height of the spike at x j equal to the distribution value b(n, p,...
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10.1 Generating Functions for Discrete Distribu- tions. A nice answer to this question, at least in the case that X has finite range, can be given in terms of the moments of X, which are numbers defined as follows:. so that a knowledge of the first two moments of X gives us its mean and variance.. Example 10.1 Suppose X...
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11.1 Introduction. The entries in the first row of the matrix P in Example 11.1 represent the proba- bilities for the various kinds of weather following a rainy day. Theorem 11.1 Let P be the transition matrix of a Markov chain. Example 11.2 (Example 11.1 continued) Consider again the weather in the Land of Oz. Table 11.1: Powers of the...
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12.1 Random Walks in Euclidean Space. In the last several chapters, we have studied sums of random variables with the goal being to describe the distribution and density functions of the sum. Definition 12.1 Let {X k. If the common range of the X k ’s is R m , then we say that { S n } is a...
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(1994), ‘Habit formation and variety seeking in a discrete choice model of recreation demand’, Journal of Agricultural and Resource Economics 19, 19–31.. Chib (1993), ‘Bayesian analysis of binary and polychotomous response data’, Journal of the American Statistical Association . Lenk (1994), ‘Modeling household purchase behavior with logistic normal regression’, Journal of the American Statistical Association . Rossi (1999), ‘Marketing models...
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When I wrote my first book, Qualitative Choice Analysis, in the mid- 1980s, the field had reached a critical juncture. Over the past twenty years, tremendous progress has been made, leading to what can only be called a sea change in the approach and methods of choice analysis. Among researchers working in the field, a definite sense of purpose and...
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Choosing one alternative necessarily implies not choosing any of the other alternatives. The decision maker necessarily chooses one of the alternatives. For example, suppose two alternatives labeled A and B are not mutually exclusive because the decision maker can choose both of the alternatives. In this case, an extra alternative can be defined as “none of the other alternatives.” The...
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The relation of the logit formula to the distri- bution of unobserved utility (as opposed to the characteristics of choice probabilities) was developed by Marley, as cited by Luce and Suppes (1965), who showed that the extreme value distribution leads to the logit formula. The mean of the extreme value distribution is not zero. The key assumption is not so...
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This distribution allows for correlations over alternatives and, as its name implies, is a generalization of the univariate extreme value distribution that is used for standard logit models. Hypothesis tests on the correlations within a GEV model can be used to examine whether the correlations are zero, which is equivalent to testing whether standard logit provides an accurate representation of...