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. |
From inside the book
Results 1-3 of 50
Page 12
... Probability Set Function Let denote the set of every possible outcome of a random experiment ; that is , is the sample space . It is our purpose to ... probability is 12 Probability and Distributions [ Ch . 1 The Probability Set Function.
... Probability Set Function Let denote the set of every possible outcome of a random experiment ; that is , is the sample space . It is our purpose to ... probability is 12 Probability and Distributions [ Ch . 1 The Probability Set Function.
Page 21
... probability set function must satisfy . Accordingly , P ( C2 | C1 ) is a probability set function , defined for subsets of C1 . It may be called the conditional probability set function , relative to the hypothesis C1 ; or the ...
... probability set function must satisfy . Accordingly , P ( C2 | C1 ) is a probability set function , defined for subsets of C1 . It may be called the conditional probability set function , relative to the hypothesis C1 ; or the ...
Page 47
... probability set function P is countably additive ; that is , P enjoys ( b ) of Definition 7 . The preceding discussion may be summarized in the following manner : A distribution function F ( x ) is a nondecreasing function of x , which ...
... probability set function P is countably additive ; that is , P enjoys ( b ) of Definition 7 . The preceding discussion may be summarized in the following manner : A distribution function F ( x ) is a nondecreasing function of x , which ...
Other editions - View all
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