## Introduction to Mathematical Statistics |

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Results 1-3 of 21

Page 59

Moreover, since o is known, the interval [É – (20/v/n), £-- (20/v/n)] has known end

points. Obviously we cannot say that 0.95 is the ... One may, of course, obtain a

90 per cent or a 99 per cent

...

Moreover, since o is known, the interval [É – (20/v/n), £-- (20/v/n)] has known end

points. Obviously we cannot say that 0.95 is the ... One may, of course, obtain a

90 per cent or a 99 per cent

**confidence interval**for u. If a were not known, the end...

Page 87

0.95; C2 C1 and, if Y, is observed to be yo, the interval (ya/c2, yo/c) serves as a

95 per cent

satisfy the above conditions. Hence (y1, y1/~/0.05) is one 95 per cent confidence

...

0.95; C2 C1 and, if Y, is observed to be yo, the interval (ya/c2, yo/c) serves as a

95 per cent

**confidence interval**for 6. It can be verified that c = V0.05 and c2 = 1satisfy the above conditions. Hence (y1, y1/~/0.05) is one 95 per cent confidence

...

Page 133

If the experimental values of X1, X2, ..., Xn are a 1, 22, ..., z, with s* = XX2, — £)*/n

, where £ =XX.co/n, then the interval 1 1 [£ – (bs/v/n – 1), 3 + (bs/v/n – 1)] is a 95

per cent

...

If the experimental values of X1, X2, ..., Xn are a 1, 22, ..., z, with s* = XX2, — £)*/n

, where £ =XX.co/n, then the interval 1 1 [£ – (bs/v/n – 1), 3 + (bs/v/n – 1)] is a 95

per cent

**confidence interval**for u for every a” > 0. ExAMPLE 1. If in the preceding...

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### Common terms and phrases

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