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Unformatted text preview: M4056 Review. October 8–10, 2010 Section I. Provide a precise mathematical definition for each of the following basic notions of mathematical statistics, and then provide an example or illustration: • Bernoulli random variable • Binomial random variable • Gamma random variable • Moment generating function • Random sample of size n from a population with distribution f X ( x ) • Sample pdf (sample pmf ) • Statistic • Sampling distribution of a statistic • Sample mean • Sample variance • Normal random variable • Chi squared random variable • Parametric family of distributions f X ( x  θ ) • Sufficient statistic • Likelihood function • Estimator • Method of moments estimator • Maximum likelihood estimator • Mean squared error (of an estimator) • Bias (of an estimator) Section II. 1. Let M be the mean of a sample of size n from a population described by a random variable X with distribution f X ( x ). Explain the difference in meaning between: • the expected value of X , • the sample mean (i.e., M itself), • the expected value of M . 2. Let S 2 be the sample variance of a sample of size n from a population described by a random variable X with distribution f X ( x ). Explain the difference in meaning between: • the variance of X , • the sample variance (i.e., S 2 itself),...
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This note was uploaded on 11/29/2011 for the course MATH 4056 taught by Professor Staff during the Fall '08 term at LSU.
 Fall '08
 Staff
 Statistics, Bernoulli, Binomial

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