## Introduction to Mathematical Statistics |

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Page 2

We now give some definitions (together with illustrative

an elementary algebra of sets adequate for our purposes. Definition 1. If each

element of a set A1 is also an element of set A2, the set A1 is called a subset of

the ...

We now give some definitions (together with illustrative

**examples**) which lead toan elementary algebra of sets adequate for our purposes. Definition 1. If each

element of a set A1 is also an element of set A2, the set A1 is called a subset of

the ...

Page 3

Then A1 and A2 have no points in common and Als) A2 = 0.

every set A, A sy. A = A and Asy 0 = 0. Definition 5. In certain discussions or

considerations the totality of all elements that pertain to the discussion can be

described.

Then A1 and A2 have no points in common and Als) A2 = 0.

**ExAMPLE**9. Forevery set A, A sy. A = A and Asy 0 = 0. Definition 5. In certain discussions or

considerations the totality of all elements that pertain to the discussion can be

described.

Page 189

In

yield £ = 0.6 and X (x, — £)* = 3.6. If the test derived in that exl ample is used, do

we accept or reject Ho: 61 – 0 at the 5 per cent significance level? 9.22.

In

**Example**1, let n is 10, and let the experimental values of the random variablesyield £ = 0.6 and X (x, — £)* = 3.6. If the test derived in that exl ample is used, do

we accept or reject Ho: 61 – 0 at the 5 per cent significance level? 9.22.

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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