## Introduction to Mathematical Statistics |

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Page 109

Then X1, X2,..., Xzo is a

consideration. Once the holes have been drilled and the diameters measured,

the 20 numbers may be used, as will be seen later, to elicit information about p

and a ".

Then X1, X2,..., Xzo is a

**random sample**from the normal distribution underconsideration. Once the holes have been drilled and the diameters measured,

the 20 numbers may be used, as will be seen later, to elicit information about p

and a ".

Page 153

Let X1, ..., Xio denote a

p, q2). Let Y = X (X. — p.)”. What is the probability l that the random interval (Y/

20.5, Y/3.25) includes the point g”? We know that Y/o” is x*(10). Moreover, the ...

Let X1, ..., Xio denote a

**random sample**of size 10 from a 10 distribution that is n(p, q2). Let Y = X (X. — p.)”. What is the probability l that the random interval (Y/

20.5, Y/3.25) includes the point g”? We know that Y/o” is x*(10). Moreover, the ...

Page 176

Let Y, & Ya & Ya be the order statistics of a

distribution having p.d. f. f(x) = e-o-'), 0 < r < co, zero elsewhere, where —oo & 0 <

oo. Determine the function c(6) of 6 so that Pr[6 : Yi < c(6)] = 0.95. From this result

...

Let Y, & Ya & Ya be the order statistics of a

**random sample**of size 3 from thedistribution having p.d. f. f(x) = e-o-'), 0 < r < co, zero elsewhere, where —oo & 0 <

oo. Determine the function c(6) of 6 so that Pr[6 : Yi < c(6)] = 0.95. From this result

...

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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