Introduction to Mathematical Statistics |
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Page 15
... sample space A = { x ; 0 < x < 1 } . If A1 = { x ; 0 < x < 4 } and A2 = { x ; ≤ x ≤ 1 } , find P ( A2 ) if P ( A1 ) = 4 . } < 1.19 . Let the sample space be ✓ = { x ; 0 < x < and P ( A2 ) = } , where A1 = { x ; 0 < x ≤ 2 } and A2 ...
... sample space A = { x ; 0 < x < 1 } . If A1 = { x ; 0 < x < 4 } and A2 = { x ; ≤ x ≤ 1 } , find P ( A2 ) if P ( A1 ) = 4 . } < 1.19 . Let the sample space be ✓ = { x ; 0 < x < and P ( A2 ) = } , where A1 = { x ; 0 < x ≤ 2 } and A2 ...
Page 17
... sample space = { x ; 0 < x < 1 } . If A1 = { x ; 0 < x < } } and A2 = { x ; < x < 1 } , find P ( A2 ) if P ( A1 ) = 4 . A2 } A 1.19 . Let the sample space be ✓ = { x ; 0 < x < = 10 } and let P ( A1 ) = } { x ; 0 < x < 4 } . and P ( A2 ) ...
... sample space = { x ; 0 < x < 1 } . If A1 = { x ; 0 < x < } } and A2 = { x ; < x < 1 } , find P ( A2 ) if P ( A1 ) = 4 . A2 } A 1.19 . Let the sample space be ✓ = { x ; 0 < x < = 10 } and let P ( A1 ) = } { x ; 0 < x < 4 } . and P ( A2 ) ...
Page 50
... sample space . This means that , for our purposes , the sample space is effectively the subset A1 . We are now confronted with the problem of defining a probability set function with A , as the " new " sample space . 2 1 Let the ...
... sample space . This means that , for our purposes , the sample space is effectively the subset A1 . We are now confronted with the problem of defining a probability set function with A , as the " new " sample space . 2 1 Let the ...
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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