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 446
... Quadratic Forms A homogeneous polynomial of degree 2 in n variables is called a quadratic form in those variables . If both the variables and the coefficients are real , the form is called a real quadratic form . Only real quadratic forms ...
... Quadratic Forms A homogeneous polynomial of degree 2 in n variables is called a quadratic form in those variables . If both the variables and the coefficients are real , the form is called a real quadratic form . Only real quadratic forms ...
Page 447
... quadratic form in the n variables X1 , X2 , ... , X. If the sample arises from a distribution that is N ( u , o2 ) , we know that the random variable nS2 / o2 is x2 ( n − 1 ) regardless of the value of μ . This fact proved useful in ...
... quadratic form in the n variables X1 , X2 , ... , X. If the sample arises from a distribution that is N ( u , o2 ) , we know that the random variable nS2 / o2 is x2 ( n − 1 ) regardless of the value of μ . This fact proved useful in ...
Page 492
... quadratic form , Xn , are dependent . 10.44 . Let X1 , X2 , X3 , X4 denote a random sample of size 4 from a distribution which is N ( 0 , 2 ) . Let YaX , where a ,, a2 , a3 , and a , are — X1X2 Σa¡X1 , where a1 , a2 , a3 , real ...
... quadratic form , Xn , are dependent . 10.44 . Let X1 , X2 , X3 , X4 denote a random sample of size 4 from a distribution which is N ( 0 , 2 ) . Let YaX , where a ,, a2 , a3 , and a , are — X1X2 Σa¡X1 , where a1 , a2 , a3 , real ...
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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