## Introduction to mathematical statistics |

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Page 76

Robert V. Hogg, Allen Thornton Craig. In a similar manner, we find that the

distribution function of Y is G(y) =

Accordingly, the p.d.f. of Y is g(2/) = 6y5. 0 < y < 1, = 0 elsewhere. Example 6. Let

a fair ...

Robert V. Hogg, Allen Thornton Craig. In a similar manner, we find that the

distribution function of Y is G(y) =

**Pr**(**Y**< y) = 0, y < 0, = y6, 0 < y < 1, = 1, 1 < 2/-Accordingly, the p.d.f. of Y is g(2/) = 6y5. 0 < y < 1, = 0 elsewhere. Example 6. Let

a fair ...

Page 181

Now Pr (X < £p) = p, where X is an item of the random sample. The sum in the ...

By this procedure, suppose it has been found that y =

probability is y that the random interval (Yt, Yy) includes the quantile of order p.

Now Pr (X < £p) = p, where X is an item of the random sample. The sum in the ...

By this procedure, suppose it has been found that y =

**Pr**(**Y**, < fp < Yj) . Then theprobability is y that the random interval (Yt, Yy) includes the quantile of order p.

Page 199

Since a/Vn = 2, then approximately Pr (-1.96 < < 1.96^ = 0.95, or Pr (X - 3.92 < M

< X + 3.92) = 0.95. Let the observed mean of the ... Let n = 100 and/> = and

suppose we wish to compute

variable ...

Since a/Vn = 2, then approximately Pr (-1.96 < < 1.96^ = 0.95, or Pr (X - 3.92 < M

< X + 3.92) = 0.95. Let the observed mean of the ... Let n = 100 and/> = and

suppose we wish to compute

**Pr**(**Y**= 48, 49, 50, 51, 52). Since Y is a randomvariable ...

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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