LECTURE NOTES on PROBABILITY and STATISTICS Eusebius …

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LECTURE NOTESonPROBABILITY and STATISTICSEusebius DoedelTABLE OF CONTENTSSAMPLE SPACES1Events5The Algebra of Events6Axioms of Probability9Further Properties10Counting Outcomes13Permutations14Combinations21CO NDITIONAL PROBABILITY45Independent Events63DISCRETE RANDOM VARIABLES71Joint distributions82Independent random variables91Conditional distributions97Expectation101Variance and Standard Deviation108Covariance110SPECIAL DISCRETE RANDOM VARIABLES118The Bernoulli Random Variable118The Binomial Random Variable120The Poisson Random Variable130CONTINUOUS RANDOM VARIABLES142Joint distributions150Marginal density functions153Independent continuous random variables158Conditional distributions161Expectation163Variance16 9Covariance175Markov s inequality181Chebyshev s inequality184SPECIAL CONTINUOUS RANDOM VARIABLES187The Uniform Random Variable187The Exponential Random Variable191The Standard Normal Random Variable196The General Normal Random Variable201The Chi-Square Random Variable206THE CENTRAL LIMIT THEOREM211SAMPLE STATISTICS24

PROBABILITY and STATISTICS Eusebius Doedel. TABLE OF CONTENTS SAMPLE SPACES 1 Events 5 The Algebra of Events 6 Axioms of Probability 9 Further Properties 10 Counting Outcomes 13 Permutations 14 Combinations 21 CONDITIONAL PROBABILITY 45 Independent Events 63 DISCRETE RANDOM VARIABLES 71 Joint distributions 82

  Statistics, Probability, Probability and statistics