Introduction to Mathematical Statistics |
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Page 18
... exists , if X is a continuous type of random variable , or such that Συ ( 2 ) f ( 2 ) exists , if X is a discrete type of random variable . The integral , or the sum , as the case may be , is called the mathematical expectation ( or ...
... exists , if X is a continuous type of random variable , or such that Συ ( 2 ) f ( 2 ) exists , if X is a discrete type of random variable . The integral , or the sum , as the case may be , is called the mathematical expectation ( or ...
Page 25
... exists , is given by Mx ( t ) = - E ( etX ) = Σetzf ( x ) ∞6etx Σ π2x2 The ratio test may be used to show that this series converges only if t≤0 . Thus there does not exist a positive number h such that Mx ( t ) exists for -h < t < h ...
... exists , is given by Mx ( t ) = - E ( etX ) = Σetzf ( x ) ∞6etx Σ π2x2 The ratio test may be used to show that this series converges only if t≤0 . Thus there does not exist a positive number h such that Mx ( t ) exists for -h < t < h ...
Page 146
... exists for h < t < h . Then the random variable Y ( Ex - - ( † X ; − nμ ) / ( √ño ) = √n ( X – 4 ) / has a limiting distribution = - - that is normal with mean zero and variance one . PROOF . Since Mx ( t ) = E ( etx ) exists for -h ...
... exists for h < t < h . Then the random variable Y ( Ex - - ( † X ; − nμ ) / ( √ño ) = √n ( X – 4 ) / has a limiting distribution = - - that is normal with mean zero and variance one . PROOF . Since Mx ( t ) = E ( etx ) exists for -h ...
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