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 45
Robert V. Hogg, Allen Thornton Craig. for the discrete type of random variable , and -S F ( x ) = f ( w ) dw , for the continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete ...
Robert V. Hogg, Allen Thornton Craig. for the discrete type of random variable , and -S F ( x ) = f ( w ) dw , for the continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete ...
Page 48
... type or of the discrete type is a constant on the space , we say that the probability is distributed uniformly over A. Thus , in the example above , we say that X has a uniform ... discrete types 48 Probability and Distributions [ Ch . 1.
... type or of the discrete type is a constant on the space , we say that the probability is distributed uniformly over A. Thus , in the example above , we say that X has a uniform ... discrete types 48 Probability and Distributions [ Ch . 1.
Page 83
... discrete type of random variable X2 , given that the discrete type of random variable X1 = x1 . In a similar manner we define the symbol ƒ112 ( x1 | x2 ) by the relation f112 ( X1X2 ) = f ( x1 , x2 ) f2 ( x2 ) f2 ( x2 ) > 0 , and we ...
... discrete type of random variable X2 , given that the discrete type of random variable X1 = x1 . In a similar manner we define the symbol ƒ112 ( x1 | x2 ) by the relation f112 ( X1X2 ) = f ( x1 , x2 ) f2 ( x2 ) f2 ( x2 ) > 0 , and we ...
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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 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 subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ σ²