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 146
... p.d.f. and distribution function of a standard normal distribution . Let Y have a truncated distribution with p.d.f. g ( y ) = q ( y ) / [ P ( b ) − P ( a ) ] , a < y < b , zero ... Distributions [ Ch . 3 The Bivariate Normal Distribution.
... p.d.f. and distribution function of a standard normal distribution . Let Y have a truncated distribution with p.d.f. g ( y ) = q ( y ) / [ P ( b ) − P ( a ) ] , a < y < b , zero ... Distributions [ Ch . 3 The Bivariate Normal Distribution.
Page 162
... p.d.f. f ( x ) = 4x3 , 0 < x < 1 , zero elsewhere . Show that Y = -2 ln X * is x2 ( 2 ) . 4.6 . Let X1 , X2 be a random sample of size n = 2 from a distribution ... distribution function 162 Distributions of Functions of Random Variables [ Ch ...
... p.d.f. f ( x ) = 4x3 , 0 < x < 1 , zero elsewhere . Show that Y = -2 ln X * is x2 ( 2 ) . 4.6 . Let X1 , X2 be a random sample of size n = 2 from a distribution ... distribution function 162 Distributions of Functions of Random Variables [ Ch ...
Page 201
... distribution having p.d.f. f ( x ) = e , 0 < x < ∞o , zero elsewhere . Find Pr ( 3≤ Y1 ) . 3 4.57 . Let X1 , X2 , X , be a random sample from a distribution of the continuous type having p.d.f. f ( x ) = 2x , 0 < x < 1 , zero ...
... distribution having p.d.f. f ( x ) = e , 0 < x < ∞o , zero elsewhere . Find Pr ( 3≤ Y1 ) . 3 4.57 . Let X1 , X2 , X , be a random sample from a distribution of the continuous type having p.d.f. f ( x ) = 2x , 0 < x < 1 , zero ...
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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. g₁(y₁ gamma distribution given Hint hypothesis H₁ 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 Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²