Introduction to Mathematical Statistics |
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Page 55
... denote a random sample from a given distribution . Let Y = u ( X1 , X2 , ... , Xn ) denote a function of X1 , X2 , ** , Xn alone . Then the random variable Y u ( X1 , X2 ... random sample will be obtained in §3.3 ] RANDOM SAMPLING 55.
... denote a random sample from a given distribution . Let Y = u ( X1 , X2 , ... , Xn ) denote a function of X1 , X2 , ** , Xn alone . Then the random variable Y u ( X1 , X2 ... random sample will be obtained in §3.3 ] RANDOM SAMPLING 55.
Page 96
... denote a random sample from a normal distribution n ( x ; 0 , 1 ) . In accordance with the theorem of Section 3.3 , page 56 , the statistic X = ( X + X2 + X2 ... + X9 ) / 9 is normal with mean • and variance 2 1/9 . Thus is an unbiased ...
... denote a random sample from a normal distribution n ( x ; 0 , 1 ) . In accordance with the theorem of Section 3.3 , page 56 , the statistic X = ( X + X2 + X2 ... + X9 ) / 9 is normal with mean • and variance 2 1/9 . Thus is an unbiased ...
Page 132
... denote two independent random samples from two independent normal distributions with the same variance o2 . m Find the constant c so that o [ Σ ( X ; − X ) 2 + [ ( Y ; ( Y. — Y ) 2 ] is an unbiased sta- - 1 - i tistic for o2 ...
... denote two independent random samples from two independent normal distributions with the same variance o2 . m Find the constant c so that o [ Σ ( X ; − X ) 2 + [ ( Y ; ( Y. — Y ) 2 ] is an unbiased sta- - 1 - i tistic for o2 ...
Contents
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