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Statistics Note
Hoeffding’s inequality: set the lower and upper bounds of confidence interval for a bounded random variable. The inequality holds for both large and small sample. Check MIT 18.650 Lecture Note Page 27. Slutsky’s theorem: replace theoretical mean with empirical mean in … Continue reading
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Kurtosis
Leotokurtic: kurtosis>3 Mesokurtic: kurtosis=3 Platyk: kurtosis<3 From wiki: http://en.wikipedia.org/wiki/Kurtosis D: Laplace distribution, also known as the double exponential distribution, red curve (two straight lines in the logscale plot), excess kurtosis = 3 S: hyperbolic secant distribution, orange curve, excess kurtosis = 2 L: logistic distribution, green … Continue reading
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Covariance matrix
The covariance matrix of random variables is an matrix that . The correlation matrix is the covariance matrix of standardized random variables . For any random variable , we have , where . So the covariance matrix is positivesemidefinite, since … Continue reading
The forth business day of the month
What is the probability that the forth business day of the month is Thursday?(forget about the holidays on weekdays) This is like asking what is the probability that the first day of the month is Sat, Sun, or Monday. So … Continue reading