## Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |

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Page 126

3.2 The

to em. Consider the function /(x) defined by mxe-m f(x) = , , x = 0,1,2,..., = 0

elsewhere, where m > 0. Since m > 0, then /(X) > 0 and x x = 0 A- x = 0 A- that is,/(

x) ...

3.2 The

**Poisson Distribution**Recall that the series converges, for all values of m,to em. Consider the function /(x) defined by mxe-m f(x) = , , x = 0,1,2,..., = 0

elsewhere, where m > 0. Since m > 0, then /(X) > 0 and x x = 0 A- x = 0 A- that is,/(

x) ...

Page 130

If the random variable X has a

), find Pr (X = 4). 3.23. The m.g.f. of a random variable X is eMe' ~ l). Show that Pr

(jx - 2a < X < n + 2a) = 0.931. 3.24. In a lengthy manuscript, it is discovered that ...

If the random variable X has a

**Poisson distribution**such that Pr (X = 1) = Pr (X = 2), find Pr (X = 4). 3.23. The m.g.f. of a random variable X is eMe' ~ l). Show that Pr

(jx - 2a < X < n + 2a) = 0.931. 3.24. In a lengthy manuscript, it is discovered that ...

Page 244

We shall find the limiting distribution of the binomial distribution, when p = n/n, by

finding the limit of M(t; n). ... Since there exists a distribution, namely the

We shall find the limiting distribution of the binomial distribution, when p = n/n, by

finding the limit of M(t; n). ... Since there exists a distribution, namely the

**Poisson****distribution**with mean that has this m.g.f. e^e' ~ ", then, in accordance with the ...### What people are saying - Write a review

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