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 84
... given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. of the continuous type of random variable X1 , given that the continuous type of random variable X2 has the value x2 ...
... given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. of the continuous type of random variable X1 , given that the continuous type of random variable X2 has the value x2 ...
Page 85
... given X1 = x1 , which can be written more simply as var ( X2 | x1 ) . It is convenient to refer to these as the " conditional mean " and the " conditional variance " of X2 , given X , = x ,. Of course , we have var ( X2 | x1 ) = E ( X } ...
... given X1 = x1 , which can be written more simply as var ( X2 | x1 ) . It is convenient to refer to these as the " conditional mean " and the " conditional variance " of X2 , given X , = x ,. Of course , we have var ( X2 | x1 ) = E ( X } ...
Page 148
... given that X = x . That is , the conditional p.d.f. of Y , given X = x , is itself normal with mean μ1⁄2 + р ( σ2 / σ1 ) ( x — μ1 ) and variance σ ( 1 − p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y ...
... given that X = x . That is , the conditional p.d.f. of Y , given X = x , is itself normal with mean μ1⁄2 + р ( σ2 / σ1 ) ( x — μ1 ) and variance σ ( 1 − p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y ...
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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