منابع مشابه
Introduction to Probability Theory
In probability theory, we are given a set Ω of outcomes ω, and try to consider the probabilities of subsets A ⊂ Ω, which we call events. To this end, we define a probability measure Pr(·) or μ(·) (we will use each notation interchangably) that is a function from these sets A ⊂ Ω → [0, 1]. As a technical complicate, μ or Pr may only be defined on some of the subsets of Ω, but this will be adress...
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Probability theory is concerned with events whose outcomes are not known ahead. Rather, the likelihoods of various outcomes are known. Formally, the set of outcomes is called a sample space S. For example, if the event is a coin flip, then S = {H,T}. If the event is the time of arrival of the next request for service at a server, then S is the nonnegative real numbers. We will be concerned with...
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Up to this point, we have only spoken of RVs as being single-dimensional objects. We will now turn to the case of vector-valued random variables, which are functions mapping a sample space into Rn. Thus, when we talk about the distribution or density of X = (X1, X2, . . . , Xn), we refer to n-dimensional real-valued functions. Alternatively, one could think of the individual elements Xi as dist...
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tatistical inference allows one to draw conclusions about the characteristics of a population on the basis of data collected from a sample of subjects from that population. Almost all the statistical inferences typically seen in the medical literature are based on probability models that connect summary statistics calculated using the observed data to estimates of parameter values in the popula...
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If a coin is tossed, then there are two possible outcomes: heads and tails. Statements such as ‘the chance that the outcome will be heads is 50%’ are formalized in probability theory, giving a better way to reason about the odds of a certain outcome of an experiment. The possible outcomes of an experiment are called the sample space. For example, the sample space of the coin tossing experiment ...
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ژورنال
عنوان ژورنال: Technometrics
سال: 1972
ISSN: 0040-1706,1537-2723
DOI: 10.1080/00401706.1972.10488996