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 88
Page 5
... Example 4. Let A , and A2 be defined as in Example 1. Then A , U A2 = A2 . Example 5. Let A2 = Ø . Then A , U A2 = A , for every set A1 . Example 6. For every set A , AUA = A. Example 7. Let 1 Ak 11 = { x + SXS1 } . < k = 1 , 2 , 3 ...
... Example 4. Let A , and A2 be defined as in Example 1. Then A , U A2 = A2 . Example 5. Let A2 = Ø . Then A , U A2 = A , for every set A1 . Example 6. For every set A , AUA = A. Example 7. Let 1 Ak 11 = { x + SXS1 } . < k = 1 , 2 , 3 ...
Page 7
... Example 16. Let be defined as in Example 14 , and let the set A The complement of A ( with respect to ✓ ) is A * = { 2 , 3 , 4 } . Example 17. Given AA . Then AA * A , A ○ A * = Ø , A ~ A = A , AA = A , and ( A * ) * = A. In the ...
... Example 16. Let be defined as in Example 14 , and let the set A The complement of A ( with respect to ✓ ) is A * = { 2 , 3 , 4 } . Example 17. Given AA . Then AA * A , A ○ A * = Ø , A ~ A = A , AA = A , and ( A * ) * = A. In the ...
Page 50
... Example 3. Let f ( x ) = { , −1 < x < 1 , zero elsewhere , be the p.d.f. of the random variable X. Define the ... example , we do not use the same symbol , without subscripts , to represent different functions . That is , in Example 2 ...
... Example 3. Let f ( x ) = { , −1 < x < 1 , zero elsewhere , be the p.d.f. of the random variable X. Define the ... example , we do not use the same symbol , without subscripts , to represent different functions . That is , in Example 2 ...
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. 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