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 146
... distribution which is N ( u , o2 ) . 3.65 . Let the random variable X have a distribution that is N ( μ , σ2 ) . ( a ) Does the random variable Y = X2 also have a normal ... Distributions [ Ch . 3 The Bivariate Normal Distribution.
... distribution which is N ( u , o2 ) . 3.65 . Let the random variable X have a distribution that is N ( μ , σ2 ) . ( a ) Does the random variable Y = X2 also have a normal ... Distributions [ Ch . 3 The Bivariate Normal Distribution.
Page 151
... bivariate normal distribution with respective parameters μx 2.8 , μy = 110 , σ = 0.16 , o 100 , and p = 0.6 . Compute : = ( a ) Pr ( 106 < y < 124 ) . ( b ) Pr ( 106 < Y < 124 | X = 3.2 ) . = 3.71 . Let X ... Bivariate Normal Distribution.
... bivariate normal distribution with respective parameters μx 2.8 , μy = 110 , σ = 0.16 , o 100 , and p = 0.6 . Compute : = ( a ) Pr ( 106 < y < 124 ) . ( b ) Pr ( 106 < Y < 124 | X = 3.2 ) . = 3.71 . Let X ... Bivariate Normal Distribution.
Page 214
... bivariate normal p.d.f. that has means equal to zero . 4.90 . Let X and Y have a bivariate normal distribution with the parameters μ1 , μ2 , σ } , σ2 , and p . Show that W = X - μ1 μι and - Z = ( Yμ2 ) p ( 02 / 01 ) ( X — μ1 ) are ...
... bivariate normal p.d.f. that has means equal to zero . 4.90 . Let X and Y have a bivariate normal distribution with the parameters μ1 , μ2 , σ } , σ2 , and p . Show that W = X - μ1 μι and - Z = ( Yμ2 ) p ( 02 / 01 ) ( X — μ1 ) are ...
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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