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PROBABILITY AND STATISTICS - ERNET

PROBABILITY AND STATISTICSMANJUNATH KRISHNAPURCONTENTS1. What is STATISTICS and what is PROBABILITY ?52. Discrete PROBABILITY spaces73. Examples of discrete PROBABILITY spaces124. Countable and uncountable175. On infinite sums196. Basic rules of probability237. Inclusion-exclusion formula258. Bonferroni s inequalities289. Independence - a first look3010. Conditional PROBABILITY and independence3111. Independence of three or more events3412. Discrete PROBABILITY distributions3513. General PROBABILITY distributions3814. Uncountable PROBABILITY spaces - conceptual difficulties3915. Examples of continuous distributions4216. Simulation4717. Joint distributions5118. Change of variable formula5419. Independence and conditioning of random variables5820. Mean and Variance6221. Makov s and Chebyshev s inequalities6722. Weak law of large numbers6823. Monte-Carlo integration6924. Central limit theorem7025. Poisson limit for rare events7326.

!are called elementary probabilities. Any subset A is called an event. For an event Awe define its probability as P(A) = P!2A p!. Any function X: !R is called a random variable. For a random variable we define its expected value or mean as E[X] = P!2 X(!)p!. All of probability in one line: Take an (interesting) probability space (;p) and an ...

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