Notes by Dave Edwards Discrete Probability
نویسنده
چکیده
Monte Carlo integration is a powerful method for computing the value of complex integrals using probabilistic techniques. This document explains the math involved in Monte Carlo integration. First I give an overview of discrete random variables. Then I show how concepts from discrete random variables can be combined with calculus to reason about continuous random variables. Finally, with a knowledge of continuous random variables, I discuss the concept of Monte Carlo integration. To get the most of our this explanation, the reader should have a knowledge of one-dimensional calculus. A background in probability should also be helpful, although I have made an attempt to explain all necessary probability as intuitively as possible.
منابع مشابه
Arrival probability in the stochastic networks with an established discrete time Markov chain
The probable lack of some arcs and nodes in the stochastic networks is considered in this paper, and its effect is shown as the arrival probability from a given source node to a given sink node. A discrete time Markov chain with an absorbing state is established in a directed acyclic network. Then, the probability of transition from the initial state to the absorbing state is computed. It is as...
متن کاملGaps in discrete random samples: extended abstract
Motivated by applications in enumerative combinatorics and the analysis of algorithms we investigate the number of gaps and the length of the longest gap in a discrete random sample from a general distribution. We obtain necessary and sufficient conditions on the underlying distribution for the gaps to vanish asymptotically (with probability 1, or in probability), and we study the limiting dist...
متن کاملA continuous approximation fitting to the discrete distributions using ODE
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...
متن کاملConditional Expectation and Martingales
This is a set of very hurriedly compiled notes. It has not been proof-checked and is likely to have some errors. These, though, should be minor errors and maybe cleared up by referring to the relevant texts. The texts that have been used in the preparation of the notes are Feller; Grimmett and Stirzaker; Goswami and Rao; David Williams; and Mitzenmacher and Upfal. The purpose behind the notes i...
متن کامل