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 12
Page 405
... testing Ho : 0 = 1 against H1 : 02 . = B 9.9 . Let X1 , X2 , ... , X , denote a random sample from a distribution having the p.d.f. f ( x ; p ) ... hypothesis Ho Sec . 9.2 ] Uniformly Most Powerful Tests 405 Uniformly Most Powerful Tests.
... testing Ho : 0 = 1 against H1 : 02 . = B 9.9 . Let X1 , X2 , ... , X , denote a random sample from a distribution having the p.d.f. f ( x ; p ) ... hypothesis Ho Sec . 9.2 ] Uniformly Most Powerful Tests 405 Uniformly Most Powerful Tests.
Page 406
... hypothesis Ho : 0 = 2 against each simple hypothesis in the composite hypothesis H1 : 0 > 2 . The preceding example affords ... testing a simple hypothesis H , against an alternative composite hypothesis H ,. It seems desirable that this ...
... hypothesis Ho : 0 = 2 against each simple hypothesis in the composite hypothesis H1 : 0 > 2 . The preceding example affords ... testing a simple hypothesis H , against an alternative composite hypothesis H ,. It seems desirable that this ...
Page 412
... test for testing Ho against H1 . 0 9.17 . Let X1 , X2 , . . . , X25 denote a random sample of size 25 from a normal distribution N ( 0 , 100 ) . Find a uniformly most powerful critical region of size a = 0.10 for testing Ho : 0 = 75 ...
... test for testing Ho against H1 . 0 9.17 . Let X1 , X2 , . . . , X25 denote a random sample of size 25 from a normal distribution N ( 0 , 100 ) . Find a uniformly most powerful critical region of size a = 0.10 for testing Ho : 0 = 75 ...
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