Introduction to Mathematical Statistics |
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Page 2
... EXAMPLE 1. Let A1 { x ; 0 ≤ x ≤ 1 } and A2 1≤x≤2 } . Here the one - dimensional set A1 is seen to be a subset of the one - dimensional set A2 ; that is , A1C A2 . Subsequently , when the dimensionality of the set is clear , we shall ...
... EXAMPLE 1. Let A1 { x ; 0 ≤ x ≤ 1 } and A2 1≤x≤2 } . Here the one - dimensional set A1 is seen to be a subset of the one - dimensional set A2 ; that is , A1C A2 . Subsequently , when the dimensionality of the set is clear , we shall ...
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... EXAMPLE 8. Let A1 = { ( x , y ) ; 0 ≤ x + y ≤ 1 } and A2 = { ( x , y ) ; 1 < x + y } . Then A1 and A2 have no points in common and A1 ~ A2 EXAMPLE 9. For every set A , AN A A and Ao Definition 5. In certain discussions or ...
... EXAMPLE 8. Let A1 = { ( x , y ) ; 0 ≤ x + y ≤ 1 } and A2 = { ( x , y ) ; 1 < x + y } . Then A1 and A2 have no points in common and A1 ~ A2 EXAMPLE 9. For every set A , AN A A and Ao Definition 5. In certain discussions or ...
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... Example 2 of this section . 9.25 . Verify equations ( 2 ) of Example 2 of this section . 9.26 . Let X1 , X2 , *** , X , be a random sample from the normal distribution n ( x ; 0 , 1 ) . Show that the likelihood ratio principle for ...
... Example 2 of this section . 9.25 . Verify equations ( 2 ) of Example 2 of this section . 9.26 . Let X1 , X2 , *** , X , be a random sample from the normal distribution n ( x ; 0 , 1 ) . Show that the likelihood ratio principle for ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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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