## Introduction to Mathematical Statistics |

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Page 255

We shall partition the sample space into a subset C and its complement C*. If the

experimental values of X1, X2,..., Xn, say, 21, r2, ..., rn, are such that the point (r1,

r2, ..., rn) e C, we shall

We shall partition the sample space into a subset C and its complement C*. If the

experimental values of X1, X2,..., Xn, say, 21, r2, ..., rn, are such that the point (r1,

r2, ..., rn) e C, we shall

**reject**the hypothesis Ho (accept the hypothesis H1).Page 284

(b) In order to make a = 0.05, show that Ho is

Ho with probability 4 (using some auxiliary random experiment). (c) If the loss

function is such that % (4,4) = % (1,1) = 0 and £(4,1) = 1 and .% (1,4) = 2, show

that ...

(b) In order to make a = 0.05, show that Ho is

**rejected**if y > 9 and, if y = 9,**reject**Ho with probability 4 (using some auxiliary random experiment). (c) If the loss

function is such that % (4,4) = % (1,1) = 0 and £(4,1) = 1 and .% (1,4) = 2, show

that ...

Page 378

CHAPTER 11 11.1 t = 3 > 2.262,

11.13 No. 11.14 qa = ** > 7.81,

Ho. 12.8 r + 6, 2n + 46. 12.9 ra(6 + ri)/[r, (r2 – 2)], r2 > 2. CHAPTER 13 13.3 (a)

exp ...

CHAPTER 11 11.1 t = 3 > 2.262,

**reject**Ho. 11.2 |t| = 2.27 × 2.145,**reject**Ho.11.13 No. 11.14 qa = ** > 7.81,

**reject**Ho. CHAPTER 12 12.5 F = 7.6 × 3.89,**reject**Ho. 12.8 r + 6, 2n + 46. 12.9 ra(6 + ri)/[r, (r2 – 2)], r2 > 2. CHAPTER 13 13.3 (a)

exp ...

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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