Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 26
Page 200
... approximately 0.954 that the random interval ( X − 1 , X + 4 ) includes μ . μ . 7.17 . Let Y be b ( 400 , 3 ) . Compute an approximate value of Pr ( 0.25 < Y / n ) . 7.18 . If Y is b ( 100 , ) , approximate the value of Pr ( Y 7.19 ...
... approximately 0.954 that the random interval ( X − 1 , X + 4 ) includes μ . μ . 7.17 . Let Y be b ( 400 , 3 ) . Compute an approximate value of Pr ( 0.25 < Y / n ) . 7.18 . If Y is b ( 100 , ) , approximate the value of Pr ( Y 7.19 ...
Page 259
... approximately . = 4 , the joint p.d.f. of X1 and X2 is 16e- ( x1 + x2 ) / 4 , O elsewhere , 1 0 < x1 < ∞ , 0 < x2 < ∞ , and Pr [ ( X1 , X2 ) ЄC ] = 1 - 9.5 9.5- 5 - x2 1 16 e- ( x1 + x2 ) / 4 dx1 dx2 0 = 0.31 approximately . Thus the ...
... approximately . = 4 , the joint p.d.f. of X1 and X2 is 16e- ( x1 + x2 ) / 4 , O elsewhere , 1 0 < x1 < ∞ , 0 < x2 < ∞ , and Pr [ ( X1 , X2 ) ЄC ] = 1 - 9.5 9.5- 5 - x2 1 16 e- ( x1 + x2 ) / 4 dx1 dx2 0 = 0.31 approximately . Thus the ...
Page 268
... approximately 0.05 and that the power of the test when 0 = 4 is approximately 0.31 . The power function K ( 0 ) of the test for all 0 ≥ 2 will now be obtained . We have - x1 [ ' - * 2 1/2 exp ( −2 , + x2 ) dx , dz2 ( - dx2 0 9.5 9.5 ...
... approximately 0.05 and that the power of the test when 0 = 4 is approximately 0.31 . The power function K ( 0 ) of the test for all 0 ≥ 2 will now be obtained . We have - x1 [ ' - * 2 1/2 exp ( −2 , + x2 ) dx , dz2 ( - dx2 0 9.5 9.5 ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²