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 179
... distribution over the interval ( —π / 2 , π / 2 ) . Show that Y tan X has a Cauchy distribution . = 2 4.29 . Let X and X2 be two independent normal random variables , each with mean ... F Distributions 179 The Beta, t, and F Distributions.
... distribution over the interval ( —π / 2 , π / 2 ) . Show that Y tan X has a Cauchy distribution . = 2 4.29 . Let X and X2 be two independent normal random variables , each with mean ... F Distributions 179 The Beta, t, and F Distributions.
Page 184
... distribution of this random variable is usually called an F - distribution ; and we often call the ratio , which we have denoted by W , F. That is , F = U / r1 V / r2 It should be observed that an F - distribution is completely ...
... distribution of this random variable is usually called an F - distribution ; and we often call the ratio , which we have denoted by W , F. That is , F = U / r1 V / r2 It should be observed that an F - distribution is completely ...
Page 185
... distribution functions of the beta and binomial distributions . 4.40 . Let T have a t - distribution with 10 degrees of freedom . Find Pr ( | T | > 2.228 ) from Table IV . 4.41 . Let T have a t - distribution with 14 ... F Distributions 185.
... distribution functions of the beta and binomial distributions . 4.40 . Let T have a t - distribution with 10 degrees of freedom . Find Pr ( | T | > 2.228 ) from Table IV . 4.41 . Let T have a t - distribution with 14 ... F Distributions 185.
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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 g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ 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 sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²