Introduction to Mathematical Statistics |
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Page 149
... ( Y - np ) / √np ( 1 - p ) √n ( x − p ) / √p ( 1 — - p ) μ ) / o has a limiting distribution that is normal with mean zero and variance one . Let n = 100 12 , and suppose we wish to compute Pr ( Y = 48 , 49 , 50 , 51 , 52 ) . Since Y ...
... ( Y - np ) / √np ( 1 - p ) √n ( x − p ) / √p ( 1 — - p ) μ ) / o has a limiting distribution that is normal with mean zero and variance one . Let n = 100 12 , and suppose we wish to compute Pr ( Y = 48 , 49 , 50 , 51 , 52 ) . Since Y ...
Page 161
... Pr [ F ( Yx ) < F ( § , ) ] = since F ( , ) = p and Z = F ( Y ) . Pr [ Zx < p ] , By Theorem 2 of Section 8.2 , page 159 , it is known that this probability does not depend upon F ( x ) ; that is , it is distribution - free . The p.d.f. ...
... Pr [ F ( Yx ) < F ( § , ) ] = since F ( , ) = p and Z = F ( Y ) . Pr [ Zx < p ] , By Theorem 2 of Section 8.2 , page 159 , it is known that this probability does not depend upon F ( x ) ; that is , it is distribution - free . The p.d.f. ...
Page 162
... y = Pr ( Y ; < ¿ p < Y ) . Then the probability is y that the random interval ( Y1 , Y ; ) includes the quantile of order p . If the experimental values of Y1 and Y , are respectively y ; and y ,, then the interval ( yi , y ; ) serves ...
... y = Pr ( Y ; < ¿ p < Y ) . Then the probability is y that the random interval ( Y1 , Y ; ) includes the quantile of order p . If the experimental values of Y1 and Y , are respectively y ; and y ,, then the interval ( yi , y ; ) serves ...
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