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 54
... integral ( or sum ) converges absolutely . Next , we shall point out some fairly obvious but useful facts about ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
... integral ( or sum ) converges absolutely . Next , we shall point out some fairly obvious but useful facts about ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
Page 138
... integral 1 = [ " exp ( −21 " ) dy . ( 글 ) -∞ This integral exists because the integrand is a positive continuous function which is bounded by an integrable function ; that is , and 0 < exp < exp ( −y + 1 ) , -∞ < y < ∞ , 2 00 exp ...
... integral 1 = [ " exp ( −21 " ) dy . ( 글 ) -∞ This integral exists because the integrand is a positive continuous function which is bounded by an integrable function ; that is , and 0 < exp < exp ( −y + 1 ) , -∞ < y < ∞ , 2 00 exp ...
Page 224
... integral C c [ " ... " exp [ tx - f ( x − μ ) ' A ( x 2 - μ ) • H ) ] dx , ⋅ dxn ( 2 ) tn ∞ ∞ Xn t2 yn = and then we shall subsequently set t1 = t2 == t , = 0 , and thus establish Equation ( 1 ) . First , we change the variables of ...
... integral C c [ " ... " exp [ tx - f ( x − μ ) ' A ( x 2 - μ ) • H ) ] dx , ⋅ dxn ( 2 ) tn ∞ ∞ Xn t2 yn = and then we shall subsequently set t1 = t2 == t , = 0 , and thus establish Equation ( 1 ) . First , we change the variables of ...
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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