## Introduction to mathematical statistics |

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Page 151

CHAPTER Interval Estimation 5.1

whose end points is a random variable, will be called a

denote a random variable and consider the event 1 < X < 2. This event is

equivalent ...

CHAPTER Interval Estimation 5.1

**Random Intervals**An interval, at least one ofwhose end points is a random variable, will be called a

**random interval**. Let Xdenote a random variable and consider the event 1 < X < 2. This event is

equivalent ...

Page 153

X10 denote a random sample of size 10 from a 10 distribution that is n(p, a2). Let

Y = 2 (Xi — m)2- What is the probability i that the

includes the point a2? We know that Y/<t2 is x2(10). Moreover, the events ...

X10 denote a random sample of size 10 from a 10 distribution that is n(p, a2). Let

Y = 2 (Xi — m)2- What is the probability i that the

**random interval**(Y/20.5, Y/3.25)includes the point a2? We know that Y/<t2 is x2(10). Moreover, the events ...

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 i 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 i the

probability is 0.954 that the

**random interval**(X — 2a/ Vn, X + 2a/ Vn) contains thefixed (but ...

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere