## Introduction to Mathematical Statistics |

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Page 55

In the first of these examples the p.a.f. of the random variable Y = X1 +

obtained; here Y is the sum of the two items of the random sample. In Example 4

we ...

In the first of these examples the p.a.f. of the random variable Y = X1 +

**X2**wasobtained; here Y is the sum of the two items of the random sample. In Example 4

we ...

**xx**, __ ( ) (1. y ) is called the mean of the random sample, and the statistic * .Page 113

XCE(X,*) = m6, * the statistic p(Y) = Yı/n =

for 0, 1 is the unique best statistic for 6. Exercises 5.26. Write the p.a.f. f(x, 0) = ***.

0 < r < co, 0 < 0 < co, zero elsewhere, in the Koopman-Pitman form. If X1,

XCE(X,*) = m6, * the statistic p(Y) = Yı/n =

**XX**,*/n, which is also a sufficient statisticfor 0, 1 is the unique best statistic for 6. Exercises 5.26. Write the p.a.f. f(x, 0) = ***.

0 < r < co, 0 < 0 < co, zero elsewhere, in the Koopman-Pitman form. If X1,

**X2**...Page 190

To illustrate, the form X1” + X1X2 +

and

quadratic form in the n variables X1,

the ...

To illustrate, the form X1” + X1X2 +

**X2*** is a quadratic form in the two variables X1and

**X2**; the form X,” + X* + X.” – 2X,**X2**is a ... –%**xx**. + ...+x,x. +...+x, X.) is aquadratic form in the n variables X1,

**X2**, ..., Xn. It was proved on page 128 thatthe ...

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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