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Statistics48

Order Statistics /joint pdf of order statistics / pdf of order statistics / joint pdf of two order statistics /pdf and cdf of first and the largest order statistics /median/sample range/ Relation between U(0,1) andBeta Order statistics are random samples listed in increasing order. I think you might be familiar with the minimum, maximum, median, and quantiles which are also the order statistics. X(1),X(2),X(3),...,X(n) are order statistics and X(k) is called as 'k'th order statistics. Joint probability density function of order statistics is the pdf of X(1) 2020. 7. 30.
Moment generating function / property / Binomial / Exponential / Normal /Bernoulli /Geometric/ Gamma/ Poisson /Chi squared/ Moment : core role in describing distributions. 1. make a moment generating function --- Mx(t)2. differentiate it 'r'th time ---M'r(t)3. t=0 --- M'r(0) = E(X^r)Moment Generating Function (MGF) :function that generates 'Moments' Properties of Moment Generating Function (MGF) 'Uniqueness' means ' If X and Y has same moment generating function, X and Y have same distribution' Joint Moment Generatin.. 2020. 7. 29.
Important Inequalities - Chebyshev Inequality, Cauchy-Schwarz Inequality <proof, applications, covariance Inequality> Chebyshev Inequality Chebyshev Inequality is one of the most important inequalities highly based on Markov's Inequality.It is easier to memorize 2nd notation to apply. proof you can easily have Chebyshev Inequality by using applications of Markov's Inequality so if you want to perfectly understand the Inequality I recognize you to study Markov's Inequality [Statistics] - Markov's Inequality 마르코프.. 2020. 7. 26.
Markov's Inequality 마르코프 부등식 Markov's Inequality Markov's Inequality is one of the most important and basic Inequalities. You can find the upper bound of probability that nonnegative random variable(X) is equal or greater than a positive constant(C). P(g(X)≥C) ≤ E(g(X))/C g(X): nonnegative function C: any positive constant 2020. 7. 23.
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