Introduction to Mathematical Statistics |
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Page 11
... define a probability set function . Definition 7. If P ( A ) is defined for a type of subset of the space A , and if ( a ) P ( A ) ≥ 0 , ( b ) P ( A , U A2 U A3 U ... ) 2 = P ( A1 ) + P ( A2 ) + P ( A3 ) + where the sets A1 , i = 1 , 2 ...
... define a probability set function . Definition 7. If P ( A ) is defined for a type of subset of the space A , and if ( a ) P ( A ) ≥ 0 , ( b ) P ( A , U A2 U A3 U ... ) 2 = P ( A1 ) + P ( A2 ) + P ( A3 ) + where the sets A1 , i = 1 , 2 ...
Page 50
... define the probability of the event A2 ? Once defined , this probability is called the conditional probability of the event A2 , relative to the hypothesis of the event A1 ; or , more briefly , the con- ditional probability of A2 ...
... define the probability of the event A2 ? Once defined , this probability is called the conditional probability of the event A2 , relative to the hypothesis of the event A1 ; or , more briefly , the con- ditional probability of A2 ...
Page 60
Robert V. Hogg, Allen Thornton Craig. We shall next extend the definition of a conditional p.d.f. If f ( x ) > 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the relation ƒ ( X2 , . . . , Xn│X1 ) - f ( x1 , x2 , ... , xn ) f1 ( x1 ) ...
Robert V. Hogg, Allen Thornton Craig. We shall next extend the definition of a conditional p.d.f. If f ( x ) > 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the relation ƒ ( X2 , . . . , Xn│X1 ) - f ( x1 , x2 , ... , xn ) f1 ( x1 ) ...
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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