Chapter 18 Review
Chapter 18 discussed Theoretical Probability and Statistical Inference. Jakob Bernoulli, wanted to be able to quantify probabilities by looking at the results observed in many similar instances. It seemed reasonably obvious to Bernoulli that the more observations one made of a given situation, the better one would be able to predict future occurrences. Bernoulli presented this ...view middle of the document...
De Moivre also made contributions in the area of Theoretical Probability. His major mathematical work, “The Doctrine of Chances,” began with a precise definition of probability. His definition stated that, “The Probability of an Event is greater or less, according to the number of Chances by which it may either happen or fail.” De Moivre used his definition in solving problems, such as the dice problem of de Mere.
Another concept discussed in this chapter is Statistical Inference. Statistical Inference is the process of drawing conclusions from data that are subject to random variation. Thomas Bayes and Pierre Laplace were the first to attempt a direct answer to the question of how to determine probability from observed frequencies. Bayes develop a theorem that states if X represents the number of times the event has happened in n trials, x the probability of its happening in a single trial, and r and s the two given probabilities, Baye’s aim was to calculate P(r<x<s|X), that is the probability that x is between r and s given X. Baye’s formula provided a start in answering the question of statistical inference. Further progress was made by Pierre Laplace using principles similar to those of Bayes.