## Introduction to Mathematical Statistics |

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Page 179

These random variables are mutually stochastically independent and each, in

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). ThusF(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

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

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. Thisstochastic 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