Intro to Probabilities in Statistics (Full Length)
More generally, I am enthusiastic about various problems in probability, such as extreme value theory, random algebraic topology, ergodic theory and financial mathematics. I am also interested in the applications of probability in statistics, actuarial science and physics.
. . . the concept of probability used in statistical science is meaningless in its own terms [and] . . . , however meaningful it might have been, its meaningfulness would nevertheless have remained fruitless because of the impossibility of gaining information from experimental results. (1957, p. 66)
These lessons on probability will include the following topics: Samples in probability, Probability of events, Theoretical probability, Experimental probability, Probability problems, Tree diagrams, Mutually exclusive events, Independent events, Dependent events, Factorial, Permutations, Combinations, Probability in Statistics, Probability and Combinatorics.Criticisms of probability in statistics. Some criticisms, in a philosophical vein, relate to the very use of probability models in statistics. For example, some writers have objected to probability because of a strict determinism in their Weltanschauung. This view is rare nowadays, with the success of highly probabilistic quantum methods in physics, and with the utility of probability models for clearly deterministic phenomena, for example, the effect of rounding errors in complex digital calculations. The deterministic critic, however, would probably say that quantum mechanics and probabilistic analysis of rounding errors are just temporary expedients, to be replaced later by nonprobabilistic approaches. For example, Einstein wrote in 1947 thatThus, finite frequentism bears certain structural similarities to theclassical interpretation, insofar as it gives equal weight to eachmember of a set of events, simply counting how many of them are‘favorable’ as a proportion of the total. The crucialdifference, however, is that where the classical interpretationcounted all the possible outcomes of a given experiment,finite frequentism counts actual outcomes. It is thuscongenial to those with empiricist scruples. It was developed by Venn(1876), who in his discussion of the proportion of births of males andfemales, concludes: “probability is nothing but thatproportion” (p. 84, his emphasis). Finite frequentism remainsthe dominant view of probability in statistics, and in the sciencesmore generally.