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 239
... limiting standard normal distribution . EXERCISES n 5.1 . Let X , denote the mean of a random sample of size n from a distribution that is N ( μ , o2 ) . Find the limiting distribution of Xn . 5.2 . Let Y , denote the first order ...
... limiting standard normal distribution . EXERCISES n 5.1 . Let X , denote the mean of a random sample of size n from a distribution that is N ( μ , o2 ) . Find the limiting distribution of Xn . 5.2 . Let Y , denote the first order ...
Page 244
... distribution that is b ( n , p ) . Suppose that the 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 of the binomial distribution , when p = μ / n , by finding the ...
... distribution that is b ( n , p ) . Suppose that the 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 of the binomial distribution , when p = μ / n , by finding the ...
Page 246
... distribution . - Hint : Redefine p to be 0.05 and 1 − p = 0.95 . 5.15 . Let the random variable Z , have a Poisson distribution with par- ameter μ = n . Show that the limiting ... Limiting Distributions [ Ch . 5 The Central Limit Theorem.
... distribution . - Hint : Redefine p to be 0.05 and 1 − p = 0.95 . 5.15 . Let the random variable Z , have a Poisson distribution with par- ameter μ = n . Show that the limiting ... Limiting Distributions [ Ch . 5 The Central Limit Theorem.
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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