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 41
... continuous or discrete types . Suppose that the space of a continuous type of random variable X is A = { x : 0 < x < ∞o } and that the p.d.f. of X is e ̄ * , xe . We shall in no manner alter the distribution of X [ that is , alter any ...
... continuous or discrete types . Suppose that the space of a continuous type of random variable X is A = { x : 0 < x < ∞o } and that the p.d.f. of X is e ̄ * , xe . We shall in no manner alter the distribution of X [ that is , alter any ...
Page 45
... continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random ...
... continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random ...
Page 84
... continuous type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. ...
... continuous type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. ...
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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