Introduction to Mathematical Statistics |
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Page 146
... approximate normal distribution to com- pute approximate probabilities concerning X , to find an approximate confidence interval for μ , and in Chapter Nine , to test certain statistical hypotheses without ever knowing what the exact ...
... approximate normal distribution to com- pute approximate probabilities concerning X , to find an approximate confidence interval for μ , and in Chapter Nine , to test certain statistical hypotheses without ever knowing what the exact ...
Page 148
... approximate normal distribution with mean zero and variance one ; and in applications we use the approximate normal p.d.f. as though it were the exact p.d.f. of √n ( X — μ ) / σ . ― Some illustrative examples , here and later , will ...
... approximate normal distribution with mean zero and variance one ; and in applications we use the approximate normal p.d.f. as though it were the exact p.d.f. of √n ( X — μ ) / σ . ― Some illustrative examples , here and later , will ...
Page 149
... approximate normal distribution with mean zero and variance one , Table I shows this probability to be approximately 0.382 . The convention of selecting the event 47.5 < Y < 52.5 , instead of , say , 47.8 < Y < 52.3 , as the event ...
... approximate normal distribution with mean zero and variance one , Table I shows this probability to be approximately 0.382 . The convention of selecting the event 47.5 < Y < 52.5 , instead of , say , 47.8 < Y < 52.3 , as the event ...
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