## 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 54

exists. Hence the existence of E[u(X)] implies that the corresponding

sum) converges absolutely. Next, we shall point out some fairly obvious but

useful facts about expectations when they exist. 1. If A; is a constant, then E(k) = k

.

exists. Hence the existence of E[u(X)] implies that the corresponding

**integral**(orsum) converges absolutely. Next, we shall point out some fairly obvious but

useful facts about expectations when they exist. 1. If A; is a constant, then E(k) = k

.

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This

is bounded by an integrable function; that is, 0 < exp I — — 1 < exp ( — |j>| + 1),

— oo<j<oo, and exp(-|j| + l)dy = 2e. To evaluate the

This

**integral**exists because the integrand is a positive continuous function whichis bounded by an integrable function; that is, 0 < exp I — — 1 < exp ( — |j>| + 1),

— oo<j<oo, and exp(-|j| + l)dy = 2e. To evaluate the

**integral**/, we note that / > 0 ...Page 224

t„ are arbitrary real numbers. We shall evaluate the

- dx) . . □ dx„, (2) and then we shall subsequently set /, = t2 = • • . = t„ = 0, and

thus establish Equation (1). First, we change the variables of integration in

t„ are arbitrary real numbers. We shall evaluate the

**integral**(x - |i)'A(x - \i) C exp t'x- dx) . . □ dx„, (2) and then we shall subsequently set /, = t2 = • • . = t„ = 0, and

thus establish Equation (1). First, we change the variables of integration in

**integral**...### What people are saying - Write a review

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