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 231
... mean and variance of 9 observations are 4 and 14 , respectively . We find that a tenth observation equals 6. Find the mean and the variance of the 10 observations . 4.155 . Draw 15 cards at random and without ... Normal Distribution 231.
... mean and variance of 9 observations are 4 and 14 , respectively . We find that a tenth observation equals 6. Find the mean and the variance of the 10 observations . 4.155 . Draw 15 cards at random and without ... Normal Distribution 231.
Page 244
... mean μ = np is the same for every n ; that is , р = μ / n , where μ is a constant . We shall find the limiting distribution ... distribution of the random variable Y1 = ( 244 [ Ch . 5 Limiting Distributions.
... mean μ = np is the same for every n ; that is , р = μ / n , where μ is a constant . We shall find the limiting distribution ... distribution of the random variable Y1 = ( 244 [ Ch . 5 Limiting Distributions.
Page 246
... mean zero and variance 1 . n n n — n 5.16 . Let S denote the variance of a random sample of size n from a distribution that is N ( u , o2 ) . It has been proved that nS / ( n - 1 ) converges in probability to o2 . Prove that S converges ...
... mean zero and variance 1 . n n n — n 5.16 . Let S denote the variance of a random sample of size n from a distribution that is N ( u , o2 ) . It has been proved that nS / ( n - 1 ) converges in probability to o2 . Prove that S converges ...
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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