Introduction to Mathematical Statistics |
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Page 13
... continuous type so that Pr ( XeA ) = - e - zdx , we have , with A = { x ; 0 < x < 1 } , Pr ( XeA ) = fore = 1 - e - 1 . EXAMPLE 4. Let X be a space A where = random variable of the continuous type with sample { x ; 0 < x < 1 } . Let the ...
... continuous type so that Pr ( XeA ) = - e - zdx , we have , with A = { x ; 0 < x < 1 } , Pr ( XeA ) = fore = 1 - e - 1 . EXAMPLE 4. Let X be a space A where = random variable of the continuous type with sample { x ; 0 < x < 1 } . Let the ...
Page 14
... type or of the continuous type , and have a distribution of that type , according as the probability set func- tion P ( A ) , A CA , is defined by P ( A ) = Pr [ ( X , Y ) εA ] = ΣΣΙ ( x , y ) , or by P ( A ) = Pr [ ( X , Y ) eA ] = ƒ ...
... type or of the continuous type , and have a distribution of that type , according as the probability set func- tion P ( A ) , A CA , is defined by P ( A ) = Pr [ ( X , Y ) εA ] = ΣΣΙ ( x , y ) , or by P ( A ) = Pr [ ( X , Y ) eA ] = ƒ ...
Page 15
... continuous type of random variable ( s ) ] or its sum [ for the discrete type of random variable ( s ) ] over all real values of its argument ( s ) is one . If f ( x ) is the p.d.f. of a continuous type of random variable X and if A is ...
... continuous type of random variable ( s ) ] or its sum [ for the discrete type of random variable ( s ) ] over all real values of its argument ( s ) is one . If f ( x ) is the p.d.f. of a continuous type of random variable X and if A is ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²