## Introduction to mathematical statistics |

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Page 337

sample from the distribution n(jj.3, a2) to compute a two-sample

denote by Ta2)3. The statistic W3 which is ... In particular, this means that W1, W2

, . . ., Wb_1 are mutually stochastically independent, provided

pb_1.

sample from the distribution n(jj.3, a2) to compute a two-sample

**T**, which wedenote by Ta2)3. The statistic W3 which is ... In particular, this means that W1, W2

, . . ., Wb_1 are mutually stochastically independent, provided

**Mx**= p2 = . . . =pb_1.

Page 349

is x2(n)- We have for the moment-generating function M(

00 1 J-oo "' J-oo (2ir)n'2VpVj x exp |^(x - rtT-^x - ji) - (X ~ tt)'V2~1(X ~ ^1 <faa . . .

dxn fi oo /• oo | _ J-oo "J-oo (277)n'V|Vj x exp [_(x-rt'V-

...

is x2(n)- We have for the moment-generating function M(

**t**) of Q the integral P 0000 1 J-oo "' J-oo (2ir)n'2VpVj x exp |^(x - rtT-^x - ji) - (X ~ tt)'V2~1(X ~ ^1 <faa . . .

dxn fi oo /• oo | _ J-oo "J-oo (277)n'V|Vj x exp [_(x-rt'V-

**Mx**-rt(l-2Qj ^ . . . ^ With V-1...

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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