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 34
Page 12
... subset of 6 , then P ( C ) is the probability that the outcome of the random experiment is an element of C. Henceforth it will be tacitly assumed that the structure of each set C is sufficiently simple to allow the computation . We have ...
... subset of 6 , then P ( C ) is the probability that the outcome of the random experiment is an element of C. Henceforth it will be tacitly assumed that the structure of each set C is sufficiently simple to allow the computation . We have ...
Page 29
... subset of A , let C be that subset of such that C = { c : ce and X ( c ) e A } . Thus C has as its elements all outcomes in for which the random variable X has a value that is in A. This prompts us to define , as we now do , Pr ( Xe A ) ...
... subset of A , let C be that subset of such that C = { c : ce and X ( c ) e A } . Thus C has as its elements all outcomes in for which the random variable X has a value that is in A. This prompts us to define , as we now do , Pr ( Xe A ) ...
Page 30
... subset of ✓ , and P ( C ) means the probability of C , a subset of % . From this point on , we shall adopt this convention and simply write P ( A ) . A C = Perhaps an additional example will be helpful . Let a coin be tossed two ...
... subset of ✓ , and P ( C ) means the probability of C , a subset of % . From this point on , we shall adopt this convention and simply write P ( A ) . A C = Perhaps an additional example will be helpful . Let a coin be tossed two ...
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