Introduction to Mathematical Statistics |
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Page 26
... distribution function F ( x ) is a nondecreasing function of x , which is everywhere continuous to the right and has F ( -∞ ) = 0 , F ( ∞ ) = 1. The probability Pr ( a ≤ X ≤ b ) is equal to the difference F ( b ) F ( a ) . If x is a ...
... distribution function F ( x ) is a nondecreasing function of x , which is everywhere continuous to the right and has F ( -∞ ) = 0 , F ( ∞ ) = 1. The probability Pr ( a ≤ X ≤ b ) is equal to the difference F ( b ) F ( a ) . If x is a ...
Page 193
... distribution function of a random variable Y by use of the definition of limiting distribution function obviously requires that we know Fn ( y ) for each positive integer n . But , as indicated in the introductory remarks of Section 7.1 ...
... distribution function of a random variable Y by use of the definition of limiting distribution function obviously requires that we know Fn ( y ) for each positive integer n . But , as indicated in the introductory remarks of Section 7.1 ...
Page 381
... distribution function , 54 Joint probability density function , 54 Law of large numbers , 81 , 149 Lehmann - Scheffé , 222 Lévy , P. , 193 Likelihood function , 243 Limiting distribution , 187 , 196 , 201 , 299 Limiting moment - generating ...
... distribution function , 54 Joint probability density function , 54 Law of large numbers , 81 , 149 Lehmann - Scheffé , 222 Lévy , P. , 193 Likelihood function , 243 Limiting distribution , 187 , 196 , 201 , 299 Limiting moment - generating ...
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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