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. |
From inside the book
Results 1-3 of 79
Page 100
... Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 < y < 1. Show that the correlation coefficient of X and Y is p = . 2.23 . Show that the variance of the conditional distribution of Y , given ...
... Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 < y < 1. Show that the correlation coefficient of X and Y is p = . 2.23 . Show that the variance of the conditional distribution of Y , given ...
Page 185
... Show that the graph of the beta p.d.f. is symmetric about the vertical line through x = if a = B. 4.39 . Show , for k S n ! = 1 , 2 , . . . , n , that - n k - 1 ( k − 1 ) ! ( n − k ) ! zk - − − k 2 * - ' ( 1 − 2 ) " ~ * dz = ' " Σ ...
... Show that the graph of the beta p.d.f. is symmetric about the vertical line through x = if a = B. 4.39 . Show , for k S n ! = 1 , 2 , . . . , n , that - n k - 1 ( k − 1 ) ! ( n − k ) ! zk - − − k 2 * - ' ( 1 − 2 ) " ~ * dz = ' " Σ ...
Page 192
... Show that Y1 , Y2 , Y3 are mutually independent . 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 X1 Y1 = Y2 = , X1 + X2 X1 + X2 + X3 Y3 = X1 + X2 + ...
... Show that Y1 , Y2 , Y3 are mutually independent . 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 X1 Y1 = Y2 = , X1 + X2 X1 + X2 + X3 Y3 = X1 + X2 + ...
Other editions - View all
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(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 W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ Σ Σ σ²