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 228
... matrix of the means and V is the positive definite covariance matrix . Let Y = c'X and Z = d'X , where X ' = [ X1 , . . . ‚ X „ ] , c ′ = [ c1 , . . . , c „ ] , and d ' = [ d1 , ... , d ] are real matrices . ( a ) Find m ( t1 , t2 ) = E ...
... matrix of the means and V is the positive definite covariance matrix . Let Y = c'X and Z = d'X , where X ' = [ X1 , . . . ‚ X „ ] , c ′ = [ c1 , . . . , c „ ] , and d ' = [ d1 , ... , d ] are real matrices . ( a ) Find m ( t1 , t2 ) = E ...
Page 485
... matrix of means μ ' [ μ1 , μ2 ] and positive definite covariance matrix V. Let = 1 X1X2 x2 X2 p2 ) 2p + o ( 1 − p2 ) σισε ( 1 – ρ ) στ ( 1 - 1 ) Show that Q , is x2 ( r , 0 ) and find r and 0. When and only when does Q1 have a central ...
... matrix of means μ ' [ μ1 , μ2 ] and positive definite covariance matrix V. Let = 1 X1X2 x2 X2 p2 ) 2p + o ( 1 − p2 ) σισε ( 1 – ρ ) στ ( 1 - 1 ) Show that Q , is x2 ( r , 0 ) and find r and 0. When and only when does Q1 have a central ...
Page 486
... matrix of nX2 , show that A = ( 1 / n ) P , where P is the nn matrix , each of whose elements is equal to one . ( b ) Demonstrate that A is idempotent and that the tr A = 1. Thus nX22 is x2 ( 1 ) . ( c ) Show that the symmetric matrix B ...
... matrix of nX2 , show that A = ( 1 / n ) P , where P is the nn matrix , each of whose elements is equal to one . ( b ) Demonstrate that A is idempotent and that the tr A = 1. Thus nX22 is x2 ( 1 ) . ( c ) Show that the symmetric matrix B ...
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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. 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 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 subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ σ²