# Introduction To Probability

## Introduction To Probability

Assignment help is an online tutoring site which caters to all the needs and requirements of the students by providing guidance of professional tutors in various fields. One such subject is statistics in which the students can seek assistance of our expert tutors. In statistics the students can get help in various sub-disciplines like introduction to probability. Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that an event will occur. This subject introduces the students to some of the basics of probability like sample spaces and events, conditional probability, and Bayes’ Theorem. Some other topics covered in the course are univariate distributions: density functions, expectation and variance, Normal, t, Binomial, Negative Binomial, Poisson, Beta, and Gamma distributions. Multivariate distributions: joint and conditional distributions, independence, transformations, and Multivariate Normal are also studied. Emphasis is also given on limit laws: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, convergence and random variables, measure theory, reasoning by representation are included in the curriculum. Families of distributions: Multivariate Normal, conjugate, marginals, mixtures and conditional distributions and expectation as well as convergence, laws of large numbers, central limit theorems, and martingales are a part of this subject.

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