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 93
Page 45
... continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random ...
... continuous type of random variable . We speak of a distribution function F ( x ) as being of the continuous or discrete type , depending on whether the random variable is of the continuous or discrete type . Remark . If X is a random ...
Page 84
... continuous type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. ...
... continuous type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X , has the value x1 . When f2 ( x2 ) > 0 , the conditional p.d.f. ...
Page 540
... continuous type with distribution function F. Compute Pr { F ( Y2 ) + [ 1 − F ( Y4 ) ] ≥ } . < 2 8 11.51 . Let Y , Y2 << Yg be the order statistics of a random sample of size n = 8 from a distribution of the continuous type with ...
... continuous type with distribution function F. Compute Pr { F ( Y2 ) + [ 1 − F ( Y4 ) ] ≥ } . < 2 8 11.51 . Let Y , Y2 << Yg be the order statistics of a random sample of size n = 8 from a distribution of the continuous type with ...
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. 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