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
... type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random variable of the continuous type , the p.d.f. f ( x ) has at most a finite number of discontinuities in every finite ...
... type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random variable of the continuous type , the p.d.f. f ( x ) has at most a finite number of discontinuities in every finite ...
Page 48
... type or of the discrete type is a constant on the space , we say that the probability is distributed uniformly over ✓ . 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 ✓ . 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 ƒ12 ( x1 | x2 ) by the relation f112 ( X1X2 ) = f ( x1 , x2 ) f2 ( x2 ) f2 ( x2 ) > 0 , and we call ...
... discrete type of random variable X2 , given that the discrete type of random variable X1 = x1 . In a similar manner we define the symbol ƒ12 ( x1 | x2 ) by the relation f112 ( X1X2 ) = f ( x1 , x2 ) f2 ( x2 ) f2 ( x2 ) > 0 , and we call ...
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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