Statistics is concerned with collecting, analyzing, interpreting, and presenting collected information. Mathematical statistics is a discipline that deals with statistics in a mathematical way of thinking. This discipline uses various theories such as probability and other branches of mathematics including linear algebra and analysis. Mathematical statistics encompasses the basic probability theories, normal distributions, probability distributions, and random variables. Mathematical statistics puts its main focus on sufficient statistics, and likelihood functions, which are the fundamental notions of statistical theory. It also entails the ideas of minimum variance unbiased estimate (MVUE), maximum likelihood estimates, Cramer-Rao inequality, and asymptotic concepts.
Mathematical statistics take in multivariate distributions, moment generating functions (MGF), transformations, and limit theorems. Discrete distributions such as negative binomials, multinomial distributions, and hypergeometric distributions. Gamma distribution, beta distributions, gamma functions, and beta functions are among the continuous distributions that are explained with important derivations. Chi-square, F distribution, t, and multivariate normal distribution are the required theoretical notions discussed in mathematical statistics.
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Statistics is a clear-cut mathematical science advancing a person’s knowledge by using empirical data demonstrated in quantitative form. Statistical analysis is defined as the collection, interpreting, and summarizing of collected information into numerical form. Finance, economics, and insurance are some application areas of statistics. Advances in statistics tool and software have made statistics application more diverse.
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