Introduction to Mathematical Statistics |
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Page 192
... Prove that Y / n converges stochastically to p . This result is one form of the law of large numbers . ( b ) Prove that 1 - Y / n converges stochastically to 1 - p . 7.6 . Let S2 denote the variance of a random sample of size n from a ...
... Prove that Y / n converges stochastically to p . This result is one form of the law of large numbers . ( b ) Prove that 1 - Y / n converges stochastically to 1 - p . 7.6 . Let S2 denote the variance of a random sample of size n from a ...
Page 352
... Prove that each of the nonzero characteristic numbers of A is equal to one if and only if A2 = A. Hint . Let L be an orthogonal matrix such that L'AL note that A is idempotent if and only if L'AL is idempotent . = diag [ a1 , a2 ,. a1 ] ...
... Prove that each of the nonzero characteristic numbers of A is equal to one if and only if A2 = A. Hint . Let L be an orthogonal matrix such that L'AL note that A is idempotent if and only if L'AL is idempotent . = diag [ a1 , a2 ,. a1 ] ...
Page 358
... Prove that X ? and every quadratic form , which is nonidentically zero in X1 , X2 , ... , X ,, are stochastically dependent . 13:12 . Let X1 , X2 , X3 , X4 denote a random sample of size 4 from a distribution which is n ( 0 , ∞2 ) ...
... Prove that X ? and every quadratic form , which is nonidentically zero in X1 , X2 , ... , X ,, are stochastically dependent . 13:12 . Let X1 , X2 , X3 , X4 denote a random sample of size 4 from a distribution which is n ( 0 , ∞2 ) ...
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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