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 185
... distribution functions of the beta and binomial distributions . 4.40 . Let T have a t - distribution with 10 degrees ... parameters r , and r2 . Prove that 1 / F has an F - distribution with parameters r2 and r1 . = 4.43 . If F has an F ...
... distribution functions of the beta and binomial distributions . 4.40 . Let T have a t - distribution with 10 degrees ... parameters r , and r2 . Prove that 1 / F has an F - distribution with parameters r2 and r1 . = 4.43 . If F has an F ...
Page 192
... distribution . Let the random variables Y1 , Y2 , Y , be defined by = X , Y , cos Y2 sin Y3 , = X2 Y , sin Y2 sin Y3 ... parameters α = X1 + X2 + α1 + • 2 ... + X , - + α , and ẞ 1 . Hint : Let Y2 = = X2 + ··· + X ,, Y3 = X3 + ··· + X ,, ...
... distribution . Let the random variables Y1 , Y2 , Y , be defined by = X , Y , cos Y2 sin Y3 , = X2 Y , sin Y2 sin Y3 ... parameters α = X1 + X2 + α1 + • 2 ... + X , - + α , and ẞ 1 . Hint : Let Y2 = = X2 + ··· + X ,, Y3 = X3 + ··· + X ,, ...
Page 372
... value of a random variable which has a gamma distribution with parameters a = r / 2 and B2 / r , where r is a positive integer . Show that X has a marginal t - distribution with r degrees of freedom . This procedure is called ...
... value of a random variable which has a gamma distribution with parameters a = r / 2 and B2 / r , where r is a positive integer . Show that X has a marginal t - distribution with r degrees of freedom . This procedure is called ...
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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