Probability Theory and Mathematical StatisticsProbability theory; Random events; Random variables; Parameters of the distribution of a Random variable; Characteristic functions; Some probability distributions; Limit theorems; Markov chains; Stochastic processes; Mathematical statistics; Sample moments and their functions; Order statistics; An outline of the theory of runs; Significance tests; The theory of estimation; Methods and schemes of sampling; An outline of analysis of variance; Theory of hypotheses testing; Elements of sequential analysis. |
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A₁ arbitrary assumption binomial distribution called characteristic function coefficient compute condition continuous type Dē(X defined Definition degrees of freedom denote density function discrete type distribution function F(x elementary events elements empirical distribution function equals equation estimate example exist expected value finite number follows formula gamma distribution hence hypothesis independent random variables inequality integral interval investigate jump points k₁ k₂ Kolmogorov large numbers law of large Let us consider limit distribution m₁ Markov chain Markov process n₁ n₂ normal distribution normal distribution N(0 o(At observed value obtain P₁ parameter Poisson distribution population probability function Problem proof Prove random event random variables X1 random vector regression relation satisfied Section sequence of random simple sample standard deviation stationary stationary process statistic stochastic process stochastically convergent Student's t-distribution Suppose t₁ tables variance X₁ Y₁ zero