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 100
... Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 < y < 1. Show that the correlation coefficient of X and Y is p = . = X , 2.23 . Show that the variance of the conditional distribution of Y ...
... Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 < y < 1. Show that the correlation coefficient of X and Y is p = . = X , 2.23 . Show that the variance of the conditional distribution of Y ...
Page 185
... Show that T2 has an F - distribution with parameters 1 and r2 = r . Hint : What is the distribution of the numerator of T2 ? 4.45 . Show that the t - distribution with r = 1 degree of freedom and the Cauchy distribution are the same ...
... Show that T2 has an F - distribution with parameters 1 and r2 = r . Hint : What is the distribution of the numerator of T2 ? 4.45 . Show that the t - distribution with r = 1 degree of freedom and the Cauchy distribution are the same ...
Page 192
... Show that Y1 , Y2 , Y3 are mutually independent . 4.49 . Let X1 , X2 , X3 be i.i.d. , each with the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Show that = X1 X1 + X 2 ' 1 Y2 = = 2 X1 + X 2 X1 + X2 + X3 Y3 ...
... Show that Y1 , Y2 , Y3 are mutually independent . 4.49 . Let X1 , X2 , X3 be i.i.d. , each with the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Show that = X1 X1 + X 2 ' 1 Y2 = = 2 X1 + X 2 X1 + X2 + X3 Y3 ...
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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 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