Week 7.ppt - HANU Probability and Statistics Copyright by...

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1 HANU Probability and Statistics Copyright by Prof. Nguyen Xuan Hoai, IT R&D Center, Hanoi University
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2 Lecture Contents Random Samples. Sampling Distribution.
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3 Random Samples Population - consists of the totality of the observations with which we are concerned. Sample – is a subset of a population.
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4 Random Samples Biased vs. Random samples Random samples :
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5 Random Samples Quantities (functions) measures over random samples are random variables. In particular: Statistic - Any function of the random variables constituting a random sample is called a statistic .
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6 Random Samples Common Statistics – Sample mean : Sample median : Sample mode : the value of the sample that most occur . e.g: 0.32 0.53 0.28 0.37 0.47 0.43 0.36 0.42 0.38 0.43.
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7 Random Samples Common Statistics – Sample variance – Sample standard deviation: Sample range: R=X max -X min
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8 Law of Large Numbers Markov Inequality: Suppose that X is a random variable such that Pr(X ≥ 0) = 1. Then for every real number t > 0,
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9 Law of Large Numbers Chebyshev Inequality: Let X be a random variable for which Var(X) exists.
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