Introduction to Mathematical Statistics |
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Page 2
... event A has occurred . Now conceive of our having made N repeated performances of the random experiment . Then we can count the number ƒ of times ( the frequency ) that the event A actually occurred throughout the N performances . The ...
... event A has occurred . Now conceive of our having made N repeated performances of the random experiment . Then we can count the number ƒ of times ( the frequency ) that the event A actually occurred throughout the N performances . The ...
Page 3
... event A in each of the following instances : ( a ) The toss of an unbiased coin where the event A is tails . ( b ) The cast of an honest die where the event A is a five or a six . ( c ) The draw of a card from an ordinary deck of ...
... event A in each of the following instances : ( a ) The toss of an unbiased coin where the event A is tails . ( b ) The cast of an honest die where the event A is a five or a six . ( c ) The draw of a card from an ordinary deck of ...
Page 32
... event E , we must assume that each of the mutually exclusive and exhaustive events A1 , A2 , ... , Ax has the same probability 1 / k . This assumption then becomes part of our probability model . Obviously , if this assumption is not ...
... event E , we must assume that each of the mutually exclusive and exhaustive events A1 , A2 , ... , Ax has the same probability 1 / k . This assumption then becomes part of our probability model . Obviously , if this assumption is not ...
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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