## Introduction to Mathematical Statistics |

### From inside the book

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Page 96

For example,

m(x; 6, 1). In accordance with the theorem of Section 3.3, page 56, the statistic X

= (X, + X, + ... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an ...

For example,

**let X1**, X2, ..., X, denote a random sample from a normal distributionm(x; 6, 1). In accordance with the theorem of Section 3.3, page 56, the statistic X

= (X, + X, + ... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an ...

Page 101

Exercises 5.10.

distribution having p.d.s. f(z; 0) = (1/6)e^*.*, 0 < r < co, 0 < 0 < co, zero elsewhere.

Show that Y = XI + X, + Xa is a sufficient statistic for 6. For convenience, let Y2 =

X2 + X, ...

Exercises 5.10.

**Let X1**, X2, X, denote a random sample of size 3 from thedistribution having p.d.s. f(z; 0) = (1/6)e^*.*, 0 < r < co, 0 < 0 < co, zero elsewhere.

Show that Y = XI + X, + Xa is a sufficient statistic for 6. For convenience, let Y2 =

X2 + X, ...

Page 114

If fiz(x1, x2) > 0, the function f(za, ..., zn|z1, z2) is defined by the relation f(zi, 22, ''',

2.) n > 2, f(za, ...

having p.d. f. f(x; 61, 62), where Yi < 0 < 31, y2 < 02 < 62. Let Y = u1(X1, X2, ..., Xn

) ...

If fiz(x1, x2) > 0, the function f(za, ..., zn|z1, z2) is defined by the relation f(zi, 22, ''',

2.) n > 2, f(za, ...

**Let X1**, X2, ..., Xn denote a random sample from a distributionhaving p.d. f. f(x; 61, 62), where Yi < 0 < 31, y2 < 02 < 62. Let Y = u1(X1, X2, ..., Xn

) ...

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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