## Introduction to Mathematical Statistics |

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Page 1

For example, if A denotes the set of real numbers a for which 0 < a. s. 1, then 34

is an element of the set A. The

by writing %.e4. More generally, aeA means that a is an element of the set A. The

...

For example, if A denotes the set of real numbers a for which 0 < a. s. 1, then 34

is an element of the set A. The

**fact**that 34 is an element of the set A is indicatedby writing %.e4. More generally, aeA means that a is an element of the set A. The

...

Page 105

Thus E[ p(Yi)] = 0, which completes the proof of

or,” = E[(Y. – 6)*] = E{[Y2 – $(Y) + b(Yi) – 61% = E{[Y2 – 4 (Yi)]?} + E([Ö(Yi) —6]*}

+ 2E{[Y2 – 4 (Yi)][ó(Yi) – 6]}. We shall show that the last term of the right-hand ...

Thus E[ p(Yi)] = 0, which completes the proof of

**fact**(i). To prove**fact**(ii), consideror,” = E[(Y. – 6)*] = E{[Y2 – $(Y) + b(Yi) – 61% = E{[Y2 – 4 (Yi)]?} + E([Ö(Yi) —6]*}

+ 2E{[Y2 – 4 (Yi)][ó(Yi) – 6]}. We shall show that the last term of the right-hand ...

Page 146

A special case of this theorem asserts the remarkable and important

, 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 ...

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 ...

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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