Introduction to Mathematical Statistics |
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Page 34
Robert V. Hogg, Allen Thornton Craig. EXERCISES ( In order to solve some of these exercises , the student must make certain assumptions . ) 1.46 . A bowl contains 16 chips of which 6 are red , 7 are white , and 3 are blue . If four chips ...
Robert V. Hogg, Allen Thornton Craig. EXERCISES ( In order to solve some of these exercises , the student must make certain assumptions . ) 1.46 . A bowl contains 16 chips of which 6 are red , 7 are white , and 3 are blue . If four chips ...
Page 145
... exercise . - = = X1 - 1 - Remark . In Exercise 4.58 of Section 4.6 , it was seen that the stochastic independence of X1 + ... EXERCISES 4.59 . Let X be the mean of a random sample of size 5 from a normal distribution with μ 0 and o2 125 ...
... exercise . - = = X1 - 1 - Remark . In Exercise 4.58 of Section 4.6 , it was seen that the stochastic independence of X1 + ... EXERCISES 4.59 . Let X be the mean of a random sample of size 5 from a normal distribution with μ 0 and o2 125 ...
Page 158
... EXERCISES = = - με H2 . 5.6 . Let the observed value of the mean X of a random sample of size 20 from a distribution ... Exercise 5.10 when it is assumed that the variances are unknown and unequal . This is a very difficult problem , and ...
... EXERCISES = = - με H2 . 5.6 . Let the observed value of the mean X of a random sample of size 20 from a distribution ... Exercise 5.10 when it is assumed that the variances are unknown and unequal . This is a very difficult problem , and ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider 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 H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions 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 theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ