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 59
Page 90
... conditional p.d.f. of X1 , given X2 = x2 , and the marginal p.d.f. of X2 . Determine : ( a ) The constants c1 and c2 . ( b ) The joint p.d.f. of X , and X2 . ( c ) Pr < X , < { | X2 = { } ) . ( d ) Pr ( ; < X , < } ) . 2.13 . Let f ( x1 ...
... conditional p.d.f. of X1 , given X2 = x2 , and the marginal p.d.f. of X2 . Determine : ( a ) The constants c1 and c2 . ( b ) The joint p.d.f. of X , and X2 . ( c ) Pr < X , < { | X2 = { } ) . ( d ) Pr ( ; < X , < } ) . 2.13 . Let f ( x1 ...
Page 91
... p.d.f. f ( x1 , x2 ) described as follows : ( X1 , X2 ) ( 0,0 ) ( 0 , 1 ) ... conditional means . Hint : Write the probabilities in a rectangular array ... p.d.f. f ( x1 ) , and the conditional p.d.f. f211 ( x2x1 ) . ( b ) Compute Pr ( X1 + ...
... p.d.f. f ( x1 , x2 ) described as follows : ( X1 , X2 ) ( 0,0 ) ( 0 , 1 ) ... conditional means . Hint : Write the probabilities in a rectangular array ... p.d.f. f ( x1 ) , and the conditional p.d.f. f211 ( x2x1 ) . ( b ) Compute Pr ( X1 + ...
Page 110
... p.d.f. of the n random variables X1 , X2 , .. . , X , just as before . Now , however , let us take any group of k ... conditional p.d.f. If f ( x1 ) > 0 , the symbol f2 ... | 1 ( X2 , ... , xn | X , ) is defined by the relation f2 ...
... p.d.f. of the n random variables X1 , X2 , .. . , X , just as before . Now , however , let us take any group of k ... conditional p.d.f. If f ( x1 ) > 0 , the symbol f2 ... | 1 ( X2 , ... , xn | X , ) is defined by the relation f2 ...
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 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 mean µ 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 sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²