Introduction to Mathematical Statistics |
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Page 179
These random variables are mutually stochastically independent and each, in
accordance with Theorem 1, has a uniform distribution on the interval (0, 1). Thus
F(X1), F(X2), ..., F(Xa) is a random sample of size n from a uniform distribution on
...
These random variables are mutually stochastically independent and each, in
accordance with Theorem 1, has a uniform distribution on the interval (0, 1). Thus
F(X1), F(X2), ..., F(Xa) is a random sample of size n from a uniform distribution on
...
Page 229
The joint p.d.f. of X1, X2,..., Xn is given, at points of positive probability density, by
n exps 3,20,..., d. 3, K(x) + š, S(r) + noso..., 0.) i = 1 = exps; p,0,..., "..): K.G.) + n,0,...
, "...] exps: S(x)] In accordance with the factorization theorem, the statistics Y = x.
The joint p.d.f. of X1, X2,..., Xn is given, at points of positive probability density, by
n exps 3,20,..., d. 3, K(x) + š, S(r) + noso..., 0.) i = 1 = exps; p,0,..., "..): K.G.) + n,0,...
, "...] exps: S(x)] In accordance with the factorization theorem, the statistics Y = x.
Page 356
In accordance with Theorem 2, Qi and Q2 are stochastically independent. This
stochastic independence immediately implies that Q2/0° is x*(r2 = r – ri). This
completes the proof when k = 2. For k > 2, the proof may be made by induction.
In accordance with Theorem 2, Qi and Q2 are stochastically independent. This
stochastic independence immediately implies that Q2/0° is x*(r2 = r – ri). This
completes the proof when k = 2. For k > 2, the proof may be made by induction.
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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere
Bibliographic information
| Title | Introduction to Mathematical Statistics Allendoerfer advanced series Series of advanced mathematics texts |
| Author | Robert V. Hogg |
| Edition | 2 |
| Publisher | Macmillan, 1965 |
| Original from | the University of California |
| Digitized | 2 Apr 2007 |
| Length | 383 pages |
| Export Citation | BiBTeX EndNote RefMan |