Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 29
Page 47
... inequality which is often called Chebyshev's inequality . This inequality will now be established . Theorem 7. Chebyshev's Inequality . Let the random variable X have a distribution of probability about which we assume only that there ...
... inequality which is often called Chebyshev's inequality . This inequality will now be established . Theorem 7. Chebyshev's Inequality . Let the random variable X have a distribution of probability about which we assume only that there ...
Page 48
... inequality is o2 , the inequality may be written Pr ( Xμ ko ) ≤ ≥ 1 k2 ' which is the desired result . Naturally , we would take the positive number k to be greater than one to have an inequality of interest . It is seen that the ...
... inequality is o2 , the inequality may be written Pr ( Xμ ko ) ≤ ≥ 1 k2 ' which is the desired result . Naturally , we would take the positive number k to be greater than one to have an inequality of interest . It is seen that the ...
Page 278
... inequality 153 co ( n ) = n -- 100 3 ln 9 < Σ . 153 100 Xi n + In 9 = 2 3 c1 ( n ) . Moreover , L ( 75 , n ) / L ... inequality Σx , ≥ c1 ( n ) leads to the 2 x 1 1 n2 rejection of H 。: 0 = 75 , and the inequality Σx , ≤ co ( n ) ...
... inequality 153 co ( n ) = n -- 100 3 ln 9 < Σ . 153 100 Xi n + In 9 = 2 3 c1 ( n ) . Moreover , L ( 75 , n ) / L ... inequality Σx , ≥ c1 ( n ) leads to the 2 x 1 1 n2 rejection of H 。: 0 = 75 , and the inequality Σx , ≤ co ( n ) ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ