http://cnx.org/content http://cnx.org/content/col10343/1.3 col10343 Introduction to Statistics 1.3 2006/03/27 09:53:51.100 US/Central 2007/10/09 05:38:06.900 GMT-5 Ewa Paszek Ewa Paszek epaszek@liv.ac.uk zaba zaba zaba Alternative Hypothesis Asymptotic Distributions of Maximum Likelihood Estimators Best critical region Biased and Unbiased Esimators Chebyshev’s Inequality Continuous Distributions Convidence Intervals Critical region for the likelihood ratio test Discrete Distributions Estimation Likelihood Function Likelihood Ratio Tests Mathematical Expectation Maximum Likelihood Estimation (MLE) Mean Most powerful test Neyman-Pearson Lemma Null Hypothesis Probability Value Random Variable Sample Size Significance level of the test Standard Deviation Standard Error of the Mean tail-end probability Test of the Equality of two Independent Normal Distributions Tests about one mean and one variance Tests about Proportions Tests of Statistical Hypotheses The Inverse Probability Method for Generating RandomVariables The Logistic Distribution Type I error Type II error Uniform pseudo_random variable generation Uniformly most powerful critical region Variance Mathematics and Statistics This course is a short series of lectures on Introductory Statistics. Topics covered are listed in the Table of Contents. The notes were prepared by Ewa Paszek and Marek Kimmel. The development of this course has been supported by NSF 0203396 grant. en Marek Kimmel Discrete Distributions DISCRETE DISTRIBUTION MATHEMATICAL EXPECTATION THE MEAN, VARIANCE, AND STANDARD DEVIATION BERNOULLI TRIALS and the BINOMIAL DISTRIBUTION GEOMETRIC DISTRIBUTION POISSON DISTRIBUTION Continuous Distributions CONTINUOUS DISTRIBUTION THE UNIFORM AND EXPONENTIAL DISTRIBUTIONS THE GAMMA AND CHI-SQUARE DISTRIBUTIONS NORMAL DISTRIBUTION THE t DISTRIBUTION Estimation Estimation CONFIDENCE INTERVALS I CONFIDENCE INTERVALS II SAMPLE SIZE Maximum Likelihood Estimation (MLE) Maximum Likelihood Estimation - Examples ASYMPTOTIC DISTRIBUTION OF MAXIMUM LIKELIHOOD ESTIMATORS Tests of Statistical Hypotheses TEST ABOUT PROPORTIONS TESTS ABOUT ONE MEAN AND ONE VARIANCE TEST OF THE EQUALITY OF TWO INDEPENDENT NORMAL DISTRIBUTIONS BEST CRITICAL REGIONS HYPOTHESES TESTING Pseudo - Numbers PSEUDO-NUMBERS PSEUDO-RANDOM VARIABLE GENERATORS, cont. THE IVERSE PROBABILITY METHOD FOR GENERATING RANDOM VARIABLES