Introduction to Mathematical Statistics |
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Page 57
... random sample of size 5 from the distribution having p.d.f. f ( x ) ( x + 1 ) / 2 , −1 < x < 1 , zero else- where , exceed zero . = - 3.26 . Let X1 , X2 , X3 be a random sample of size 3 from a normal distribution n ( x ; 6 , 4 ) ...
... random sample of size 5 from the distribution having p.d.f. f ( x ) ( x + 1 ) / 2 , −1 < x < 1 , zero else- where , exceed zero . = - 3.26 . Let X1 , X2 , X3 be a random sample of size 3 from a normal distribution n ( x ; 6 , 4 ) ...
Page 130
Robert V. Hogg, Allen Thornton Craig. Next let X and Y denote stochastically independent random variables having normal distributions n ( x ; μ1 , σ12 ) and n ( y ; μ2 , σ22 ) , respectively . The four parameters μ1 , M2 , 012 , σ22 are ...
Robert V. Hogg, Allen Thornton Craig. Next let X and Y denote stochastically independent random variables having normal distributions n ( x ; μ1 , σ12 ) and n ( y ; μ2 , σ22 ) , respectively . The four parameters μ1 , M2 , 012 , σ22 are ...
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... random sample of size 25 from a normal dis- tribution n ( x ; 0 , 100 ) . Find a uniformly most powerful critical region of size απ 0.10 for testing H 。: 0 = 75 against H1 : 0 > 75 . 9.19 . Let X1 , X2 , ... , Xn denote a random sample ...
... random sample of size 25 from a normal dis- tribution n ( x ; 0 , 100 ) . Find a uniformly most powerful critical region of size απ 0.10 for testing H 。: 0 = 75 against H1 : 0 > 75 . 9.19 . Let X1 , X2 , ... , Xn denote a random sample ...
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CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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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