## Introduction to Mathematical Statistics |

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Page 30

Suppose it is reasonable to

interval A is a subset of 3/, the probability of the event A is proportional to the

length of A. Hence if A is the interval [a, aj, a s b, then P(A) = Pr(X e A) = Pr(a • X ...

Suppose it is reasonable to

**assume**, from the nature of the experiment, that, if aninterval A is a subset of 3/, the probability of the event A is proportional to the

length of A. Hence if A is the interval [a, aj, a s b, then P(A) = Pr(X e A) = Pr(a • X ...

Page 32

It should be emphasized that in order to assign, in this manner, the probability r/k

to the event E, we must

exhaustive events A1, A2, ..., Ak has the same probability 1/k. This assumption

then ...

It should be emphasized that in order to assign, in this manner, the probability r/k

to the event E, we must

**assume**that each of the mutually exclusive andexhaustive events A1, A2, ..., Ak has the same probability 1/k. This assumption

then ...

Page 135

Momentarily we

Let z = wi(y1, y2, ..., ya), i = 1, 2, ..., n, denote the inverse functions and let J

denote the Jacobian. Under this transformation the Display (1) becomes (2) ...

Momentarily we

**assume**that these functions define a one-to-one transformation.Let z = wi(y1, y2, ..., ya), i = 1, 2, ..., n, denote the inverse functions and let J

denote the Jacobian. Under this transformation the Display (1) becomes (2) ...

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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