## Introduction to Mathematical Statistics |

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Page 151

Robert V. Hogg. C H A P T E R 5 Interval Estimation 5.1

interval, at least one of whose end points is a random variable, will be called a

2.

Robert V. Hogg. C H A P T E R 5 Interval Estimation 5.1

**Random Intervals**Aninterval, at least one of whose end points is a random variable, will be called a

**random interval**. Let X denote a random variable and consider the event 1 < X →2.

Page 153

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

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 154

Suppose we are willing to accept as a fact that the outcome X of a random

experiment is a random variable that has a ... 152, it was found that 1. the

probability is 0.954 that the

fixed (but ...

Suppose we are willing to accept as a fact that the outcome X of a random

experiment is a random variable that has a ... 152, it was found that 1. the

probability is 0.954 that the

**random interval**(X – 20/v/n, X + 20/v/n) contains thefixed (but ...

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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