## Introduction to Mathematical Statistics |

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Page 61

Let X1, X2, and Xa denote

hearts, and the number of diamonds that appear among the five cards. (a)

Determine the joint p.d.f. of X, X2, and Xa. (b) Find the marginal probability

density ...

Let X1, X2, and Xa denote

**respectively**the number of spades, the number ofhearts, and the number of diamonds that appear among the five cards. (a)

Determine the joint p.d.f. of X, X2, and Xa. (b) Find the marginal probability

density ...

Page 142

4.45. Let Xi and X2 be stochastically independent random variables. Let Xi and Y

= X1 + X2 have chi-square distributions with r1 and r degrees of freedom

degrees ...

4.45. Let Xi and X2 be stochastically independent random variables. Let Xi and Y

= X1 + X2 have chi-square distributions with r1 and r degrees of freedom

**respectively**. Here r1 < r. Show that X2 has a chi-square distribution with r — ridegrees ...

Page 148

The mean and the variance of the linear function Y = S \,x, 1 are

Pty = X ki. and The following corollary of this theorem is quite useful. Corollary.

Let X1, ..., Xn denote the items of a random sample of size n from a distribution

that ...

The mean and the variance of the linear function Y = S \,x, 1 are

**respectively**nPty = X ki. and The following corollary of this theorem is quite useful. Corollary.

Let X1, ..., Xn denote the items of a random sample of size n from a distribution

that ...

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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