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 43
Page 2
... random experiment , and the collection of every possible outcome is called the experimental 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 ...
... random experiment , and the collection of every possible outcome is called the experimental 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 ...
Page 12
... random experiment ; that is , is the sample space . It is our purpose to define a set function P ( C ) such that if C is a subset of % , then P ( C ) is the probability that the outcome of the random experiment is an element of C ...
... random experiment ; that is , is the sample space . It is our purpose to define a set function P ( C ) such that if C is a subset of % , then P ( C ) is the probability that the outcome of the random experiment is an element of C ...
Page 296
... random experiment is an element of the set A. The random experiment is to be repeated n independent times and X , will represent the number of times the outcome is an element of the set A. That is , X1 , X2 , . . X = n - X are the ...
... random experiment is an element of the set A. The random experiment is to be repeated n independent times and X , will represent the number of times the outcome is an element of the set A. That is , X1 , X2 , . . X = n - X are the ...
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 Find the p.d.f. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²