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 2
... space or the sample space . Example 1. In the toss of a coin , let the outcome tails be denoted by T and let the outcome heads be denoted by H. If we assume that the coin may be repeatedly tossed under the same conditions , then the ...
... space or the sample space . Example 1. In the toss of a coin , let the outcome tails be denoted by T and let the outcome heads be denoted by H. If we assume that the coin may be repeatedly tossed under the same conditions , then the ...
Page 20
... sample space is effectively the subset C1 . We are now confronted with the problem of defining a probability set function with C , as the " new " sample space . Let the probability set function P ( C ) be defined on the sample space and ...
... sample space is effectively the subset C1 . We are now confronted with the problem of defining a probability set function with C , as the " new " sample space . Let the probability set function P ( C ) be defined on the sample space and ...
Page 28
... sample space consists of four ordered pairs : TT , TH , HT , HH . Making certain assumptions , compute the probability of each of these ordered pairs . What is the probability of at least one head ? 1.5 Random Variables of the Discrete ...
... sample space consists of four ordered pairs : TT , TH , HT , HH . Making certain assumptions , compute the probability of each of these ordered pairs . What is the probability of at least one head ? 1.5 Random Variables of the Discrete ...
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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