## Introduction to Mathematical Statistics |

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Page 58

Since o is a known number, each of the random variables X – (20/v/n) and X + (

20/v/n) is a statistic. The interval [X – (20/v/n), X + (20/v/n)] is called a

.

Since o is a known number, each of the random variables X – (20/v/n) and X + (

20/v/n) is a statistic. The interval [X – (20/v/n), X + (20/v/n)] is called a

**random****interval**: that is, an interval at least one * of whose endpoints is a random variable.

Page 59

However, the fact that we had such a high degree of probability, prior to the

performance of the experiment, that the

includes the fixed point (parameter) u, leads us to have some reliance on the ...

However, the fact that we had such a high degree of probability, prior to the

performance of the experiment, that the

**random interval**[X – (20/v/n), X + (20/v/n)]includes the fixed point (parameter) u, leads us to have some reliance on the ...

Page 61

performed, and it is found that X1 = 21, X2 = z2, ..., Xn = 2n, then the particular

stochastically independent

distribution with ...

performed, and it is found that X1 = 21, X2 = z2, ..., Xn = 2n, then the particular

**interval**n n Xz, -o), X.G. - ). ... show (in particular) that the sum of n mutuallystochastically independent

**random**variables, each having a chi-squaredistribution with ...

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Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere