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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Results 1-3 of 78
Page 100
... Show that the correlation coefficient of X and Y is p = 1⁄2 . 2.23 . Show that the variance of the conditional distribution of Y , given X = x , in Exercise 2.22 , is ( 1 - x ) 2/12 , 0 < x < 1 , and that the variance of the conditional ...
... Show that the correlation coefficient of X and Y is p = 1⁄2 . 2.23 . Show that the variance of the conditional distribution of Y , given X = x , in Exercise 2.22 , is ( 1 - x ) 2/12 , 0 < x < 1 , and that the variance of the conditional ...
Page 185
... Show that the graph of the beta p.d.f. is symmetric about the vertical line through x = 4.39 . Show , for k [ , 1 n ! if a = B. = 1 , 2 , n , that zk - ' ( 1 − z ) " - k dz ( k - 1 ) ! ( nk ) ! - - - n k - 1 Σ ( ) σα | pˇ ( 1 − p ) ...
... Show that the graph of the beta p.d.f. is symmetric about the vertical line through x = 4.39 . Show , for k [ , 1 n ! if a = B. = 1 , 2 , n , that zk - ' ( 1 − z ) " - k dz ( k - 1 ) ! ( nk ) ! - - - n k - 1 Σ ( ) σα | pˇ ( 1 − p ) ...
Page 192
... Show that Y1 , Y2 , Y , are mutually independent . 2 4.49 . Let X1 , X2 , X3 be i.i.d. , each with the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Show that Y1 = X1 X1 + X2 ' Y2 = X + X2 X1 + X 2 + X3 ' Y3 ...
... Show that Y1 , Y2 , Y , are mutually independent . 2 4.49 . Let X1 , X2 , X3 be i.i.d. , each with the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Show that Y1 = X1 X1 + X2 ' Y2 = X + X2 X1 + X 2 + X3 ' Y3 ...
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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 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