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 33
... x x = 1 , 2 , 3 , ... , elsewhere . From such a function , we see that the space is clearly the set of positive integers which is a discrete set of points . Thus the ... X is = { Sec . 1.5 ] Random Variables of the Discrete Type 33.
... x x = 1 , 2 , 3 , ... , elsewhere . From such a function , we see that the space is clearly the set of positive integers which is a discrete set of points . Thus the ... X is = { Sec . 1.5 ] Random Variables of the Discrete Type 33.
Page 91
... random a point from the interval ( 0 , 1 ) and let the random variable X ... ( xX > xo ) is a p.d.f. ( b ) Let f ( x ) = e ̄ * , 0 < x < ∞ , and zero Pr ... variables . Let X and Y have joint p.d.f. f ( x , y ) . If u ( x , y ) is a ...
... random a point from the interval ( 0 , 1 ) and let the random variable X ... ( xX > xo ) is a p.d.f. ( b ) Let f ( x ) = e ̄ * , 0 < x < ∞ , and zero Pr ... variables . Let X and Y have joint p.d.f. f ( x , y ) . If u ( x , y ) is a ...
Page 158
... X X = = n i = 1 n is called the mean of the random sample , and the statistic S2 = ( X ; - x ) 2 i = 1 n = n Σ x2 x2 i = 1 n is called the variance of the random sample ... random 158 Distributions of Functions of Random Variables [ Ch . 4.
... X X = = n i = 1 n is called the mean of the random sample , and the statistic S2 = ( X ; - x ) 2 i = 1 n = n Σ x2 x2 i = 1 n is called the variance of the random sample ... random 158 Distributions of Functions of Random Variables [ Ch . 4.
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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 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