## Introduction to Mathematical Statistics |

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Page 153

Let X1, ..., Xio

p, q2). Let Y = X (X. — p.)”. What is the probability l that the random interval (Y/

20.5, Y/3.25) includes the point g”? We know that Y/o” is x*(10). Moreover, the ...

Let X1, ..., Xio

**denote a random**sample of size 10 from a 10 distribution that is n(p, q2). Let Y = X (X. — p.)”. What is the probability l that the random interval (Y/

20.5, Y/3.25) includes the point g”? We know that Y/o” is x*(10). Moreover, the ...

Page 170

69, to distributions of more than two random variables, it is seen that the order

statistics, unlike the items of the random sample, are stochastically dependent.

Example 1. Let X

...

69, to distributions of more than two random variables, it is seen that the order

statistics, unlike the items of the random sample, are stochastically dependent.

Example 1. Let X

**denote a random**variable of the continuous type with p.d. f. f(z)...

Page 267

Let the random variable X have the p.d. f. f(x; 6) = (1/6)e^*", 0 < r < oo, zero

elsewhere. Consider the simple hypothesis Ho: 6 = 0 = 2 and the alternative

hypothesis H1: 0 = 0" = 4. Let X1, X2

...

Let the random variable X have the p.d. f. f(x; 6) = (1/6)e^*", 0 < r < oo, zero

elsewhere. Consider the simple hypothesis Ho: 6 = 0 = 2 and the alternative

hypothesis H1: 0 = 0" = 4. Let X1, X2

**denote a random**sample of size 2 from this...

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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