Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 58
... A2 , A3 , ... , then E ( X ) = a1 f ( a1 ) + a2 ƒ ( a2 ) + a3 f ( az ) + · · · · This sum of products is seen to be ... variance of X ( or the variance of the distribution ) . - 1 The variance of X will be denoted by o2 , and we define ...
... A2 , A3 , ... , then E ( X ) = a1 f ( a1 ) + a2 ƒ ( a2 ) + a3 f ( az ) + · · · · This sum of products is seen to be ... variance of X ( or the variance of the distribution ) . - 1 The variance of X will be denoted by o2 , and we define ...
Page 222
... a2 , b1 , b2 , and the parameters of the distribution . 4.120 . Let X1 , X2 , ... , X , be a random sample of size n from a distribution which has mean μ and variance o2 . Use Chebyshev's inequality to show , for every € > 0 , that lim ...
... a2 , b1 , b2 , and the parameters of the distribution . 4.120 . Let X1 , X2 , ... , X , be a random sample of size n from a distribution which has mean μ and variance o2 . Use Chebyshev's inequality to show , for every € > 0 , that lim ...
Page 381
... a2 [ In L ( 0 ) ] a2 [ ln L ( 0 ) ] 202 002 Let us rewrite this equation as ... variance I ( 0 ) , the numerator of the right - hand member of Equation ( 1 ) ... variance 1 / nI ( 0 ) . The preceding result means that in a regular case of ...
... a2 [ In L ( 0 ) ] a2 [ ln L ( 0 ) ] 202 002 Let us rewrite this equation as ... variance I ( 0 ) , the numerator of the right - hand member of Equation ( 1 ) ... variance 1 / nI ( 0 ) . The preceding result means that in a regular case of ...
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Common terms and phrases
A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²