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Extra info for Markov Chains
For example, an economist might wish to learn about the economic condition of Appalachian farmers. He ﬁrst deﬁnes the population. Involved in this is specifying the geographical area “Appalachia” and deciding whether a “farmer” is the person who owns land suitable for farming, the person who works on it, or the person who makes managerial decisions about how the land is to be used. The economist’s decision depends on the group in which he is interested. After he has speciﬁed the population, he must decide on the variable or variables, that characteristic or set of characteristics of these people, that will give him information about their economic condition.
2. p(y) ¼ 1, that is, the sum of p( y) over all values of y is 1. y Note that in the baby cereal example these two conditions are satisﬁed. There are many functions that satisfy these two conditions. 1, examples A through D represent discrete probability distributions. In example D the random variable has a countable inﬁnity of values, and p( y) can be given by the formula p( y) ¼ (1/2)y. In many cases it is possible to represent the probability function by a formula. It is not difﬁcult to ﬁnd functions with the two properties required for a probability function.
Cross section of mine tunnel. curve; the proportion, or probability, is 1/4. The probability of debris between 0 and 95 is given by the area under the curve and to the left of 95. 5).