Limit theorems for sums of independent random variables
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Abstract
As the introduction to this thesis has described it the significant content of the thesis is a consideration of the more important aspects of the theory of limiting distributions for the distributions associated with sequences of sums of independent random variables.
We begin our analysis with the discussion of the relatively common probability law, the binomial probability law. This is defined and related to two further probability laws: the normal law and the Poisson law. It is shown that in the binomial situation when the number, n, of trials approaches infinity and the probability, p, of success at each trial approaches 0 in such a way that the variable lambda = np remains bounded, the Poisson approximation to the binomial is a uniform approximation. The DeMoivre - Laplace Limit theorem enables us to see the relation of the normal law to the binomial law. It states that the binomial distribution converges to the normal distribution in the situation wherein we are holding p constant and allowing n -> infinity. It is also noted that under favorable conditions the Poisson distribution is itself approximated by means of the Normal distribution [TRUNCATED].
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Thesis (M.A.)--Boston University.
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