Introduction to Mathematical Statistics |
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Page 85
... Consider a probability such as Pr ( a < X1 X2 < b , a < X < b ) . This probability is given by since b = S * S * ƒ “ ƒ ( x1 ) f ( x2 ) ƒ ( x3 ) dx , dï1⁄2 dx3 = 0 , ανα X2 Ss f ( x1 ) dx1 is defined in calculus to be zero . As in the ...
... Consider a probability such as Pr ( a < X1 X2 < b , a < X < b ) . This probability is given by since b = S * S * ƒ “ ƒ ( x1 ) f ( x2 ) ƒ ( x3 ) dx , dï1⁄2 dx3 = 0 , ανα X2 Ss f ( x1 ) dx1 is defined in calculus to be zero . As in the ...
Page 178
... Consider a normal distribution of the form n ( x ; 0 , 4 ) . The null simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 : > > 0 is accepted if , and only if , the observed mean ≈ of a random sample ...
... Consider a normal distribution of the form n ( x ; 0 , 4 ) . The null simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 : > > 0 is accepted if , and only if , the observed mean ≈ of a random sample ...
Page 192
... consider each row as being a random sample of size b from the given distribution ; and we may consider each column as being a random sample of size a from the given distribution . We now define a + b + 1 statistics . They are Xij and ...
... consider each row as being a random sample of size b from the given distribution ; and we may consider each column as being a random sample of size a from the given distribution . We now define a + b + 1 statistics . They are Xij and ...
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