## Introduction to Mathematical Statistics |

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Page 53

This follows from the extension of the multiplication rule. In this computation, the

assumptions that are involved seem clear.

of these

...

This follows from the extension of the multiplication rule. In this computation, the

assumptions that are involved seem clear.

**EXERCISES**(In order to solve certainof these

**exercises**, the student is required to make assumptions.) 2.1. If P(A1) > 0...

Page 145

The determination of the p.d.f. of S4 is left as an

4.58 of Section 4.6, it was seen that the stochastic independence of X1 + X2 and

XI – X2 implied, under our conditions, that the distribution from which the sample

...

The determination of the p.d.f. of S4 is left as an

**exercise**. Remark. In**Exercise**4.58 of Section 4.6, it was seen that the stochastic independence of X1 + X2 and

XI – X2 implied, under our conditions, that the distribution from which the sample

...

Page 158

A consideration of the difficulty encountered when the unknown variances of the

two independent normal distributions are not equal is assigned to one of the

...

A consideration of the difficulty encountered when the unknown variances of the

two independent normal distributions are not equal is assigned to one of the

**exercises**. Example 3. It may be verified that if in the preceding discussion n = 10,...

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### Common terms and phrases

accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere