Introduction to Statistics and Probability
Naive set theory; Probability; Random variables: discrete case; Random variables: continuous and mixed cases; Moments; Sums of random variables and limit laws; An example of statistical analysis; Point estimation and statistical inference principles; Tests of hypotheses; Interval estimation; Ranking and selection procedures; Decision theory; Nonparametric statistical inference; Regression and linear statistical inference.
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absolutely continuous Assumption asymptotically Bayes rule binomial called cells Chapter Chebyshev's Inequality choose confidence interval consider convex set decision problem decision rules decision theory defined denote density function discrete Equation essentially complete class example exists Figure finite follows fx(x given graph Hence Hint hypothesis hypothesis-testing problem independent r.v.'s integer Khinchin's Theorem Let X1 minimal essentially complete minimal sufficient statistic minimax multivariate Neyman-Pearson Lemma normal distribution Note º º observations obtain otherwise P(CS parameter Poisson population Poſ probability function procedure Prove random variables regression regular estimation reject result risk function risk points sample space Section selection smallest ſº specified statistical decision problem Student's t-distribution subset sufficient statistic Table unbiased estimator unknown Var(X variance vectors Xn are independent