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## Main Question or Discussion Point

So I have the option of either taking a year long sequence in probability theory or a year long sequence in mathematical statistics. Both require real analysis so both will be at the 'measure theoretic' level. I'm interested in these classes as they relate to computer science and specifically AI: data mining, NLP, gaming etc. Which sequence would you all suggest as more important for these applications? Thanks.

Probability Theory:

-Probability measures; Borel fields; conditional probabilities, sums of independent random variables; limit theorems; zero-one laws; stochastic processes

Mathematical Statistics:

-Statistical models, sufficiency, efficiency, optimal estimation, least squares and maximum likelihood, large sample theory Hypothesis testing and confidence intervals, one-sample and two-sample problems. Bayes theory, statistical decision theory, linear models and regression. Nonparametrics: tests, regression, density estimation, bootstrap and jackknife.

Probability Theory:

-Probability measures; Borel fields; conditional probabilities, sums of independent random variables; limit theorems; zero-one laws; stochastic processes

Mathematical Statistics:

-Statistical models, sufficiency, efficiency, optimal estimation, least squares and maximum likelihood, large sample theory Hypothesis testing and confidence intervals, one-sample and two-sample problems. Bayes theory, statistical decision theory, linear models and regression. Nonparametrics: tests, regression, density estimation, bootstrap and jackknife.