## Introduction to Mathematical Statistics |

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Page 105

accordingly Moreover a sty,)” = E{d}(Yi) – 6]*} so that the variance of the unbiased

statistic Y2 may be written a y,” = E{[Y2 – 4 (Yi)]*} + geq.)”. Now Ya is not a

function of Yi ...

**Hence**so [y* - $(yi)]h(yolyl) dy, = 0 -oo E{[Y2 – 4 (Yi)][Ö(Yi) – 6]} = 0. andaccordingly Moreover a sty,)” = E{d}(Yi) – 6]*} so that the variance of the unbiased

statistic Y2 may be written a y,” = E{[Y2 – 4 (Yi)]*} + geq.)”. Now Ya is not a

function of Yi ...

Page 146

A special case of this theorem asserts the remarkable and important fact that if X1

, X2, ..., Xn denote the items of a random sample of size n from any distribution

having finite variance o” (and

A special case of this theorem asserts the remarkable and important fact that if X1

, X2, ..., Xn denote the items of a random sample of size n from any distribution

having finite variance o” (and

**hence**finite mean u), then the random variable ...Page 198

unspecified, against all possible alternatives may be based on an F statistic. The

constant c is so selected as to yield the desired value of a. Exercises 10.5. Let ui,

u, us ...

**Hence**the test of the null composite hypothesis Ho: ui = u2 = ... = us = u, uunspecified, against all possible alternatives may be based on an F statistic. The

constant c is so selected as to yield the desired value of a. Exercises 10.5. Let ui,

u, us ...

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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