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 92
... correlation coefficient of X and Y. If the standard deviations are positive , the correlation coefficient of any two random variables is defined to be the covariance of the two random variables divided by the product of the standard ...
... correlation coefficient of X and Y. If the standard deviations are positive , the correlation coefficient of any two random variables is defined to be the covariance of the two random variables divided by the product of the standard ...
Page 222
... correlation coefficients P12 0.3 , P130.5 , and P23 0.2 . Find the correlation coefficient of the linear functions Y = X + X2 and Z = X2 + X3 . 4.122 . Find the variance of the sum of 10 random variables if each has variance 5 and if ...
... correlation coefficients P12 0.3 , P130.5 , and P23 0.2 . Find the correlation coefficient of the linear functions Y = X + X2 and Z = X2 + X3 . 4.122 . Find the variance of the sum of 10 random variables if each has variance 5 and if ...
Page 478
... correlation coefficient p . We wish to test the hypothesis that X and Y are independent . Because two jointly ... correlation coefficient of the random sample . The likelihood ratio principle , which calls for the rejection of Ho if 2 ...
... correlation coefficient p . We wish to test the hypothesis that X and Y are independent . Because two jointly ... correlation coefficient of the random sample . The likelihood ratio principle , which calls for the rejection of Ho if 2 ...
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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. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. 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 X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²