Ma 494 Theoretical Statistics
Solutions for Problem Set #4 Due March 3, 2010
Prof. Sawyer Washington University
NOTE: 5 problems on 2 pages.
1. Note P X n (2.5, 3.5) = P |X3| < 0.50 0.99 is equivalent to P |X3| >
0.50 0.01. Since Xi are N (3, 1), X is N (
Ma 494 Theoretical Statistics
Solutions for Problem Set #5 Due March 24, 2010
Prof. Sawyer Washington University
NOTE: 5 problems on 4 pages.
1. (i) p = M/N = 0.94 for N = 1000 simulated samples of size n. By Theorem 5.3.1 on page 369 of the text (with X
Ma 494 Theoretical Statistics
Solutions for Problem Set #3 Due February 22, 2010
Prof. Sawyer Washington University
1. By the hint and Denition 4.6.2 p329, Yi are gamma distributed with parameters r and = 1/, in the notation of Section 4.6 p329. Thus by T
Ma 494 Theoretical Statistics
Solutions for Final May 10, 2010
Prof. Sawyer Washington University
Seven problem solutions on four pages. Closed book and closed notes. Two 8 1 11
2
sheets of paper with notes on both sides and a calculator are allowed. Part
Ma 494 Theoretical Statistics
Solutions for Problem Set #6 Due April 30, 2010
Prof. Sawyer Washington University
NOTE: 5 problems on 3 pages. Dierent parts of problems may not be equally
weighted.
1. From the text (page 574), SY = 0.20 and SX = 0.37. Thus
Minimum-RMS Quadratic Estimators
of a Variance
S. Sawyer Washington University August 23, 2003
Assume that X1 , X2 , . . . , Xn are independent and identically distributed ran4
dom variables with E(Xi ) = , Var(Xi ) = 2 , and E(Xi ) < . Suppose
that we ar
Risk, Scores, Fisher Information, and GLRTs
(Supplementary Material for Math 494)
Stanley Sawyer Washington University
Vs. April 24, 2010
Table
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of Contents
Statistics and Esimatiors
Unbiased Estimators, Risk, and Relative Risk
S
9
Math 494 ' Name:
Spring 2014 Mldterm II 11);
1. (4 points) True / False. Please read the statements carefully, as no partial
credit will be given.
t...
(a) lg All unbiased estimators are eonsistent.
(b) E A consistent estimator must be the maxim
Ma 494 Theoretical Statistics
Test #2 Solutions for April 14, 2010
Prof. Sawyer Washington University
Take-home examination. Open book and notes. Due at end of period on 04/14/2010.
Six (6) problems on 3 pages. Not all parts of problems will be equally we
Ma 494 Theoretical Statistics
Solutions for Test #1 February 19, 2009
Prof. Sawyer Washington University
Closed book and closed notes. One 8 1 11 sheet of paper with notes on both sides
2
and a calculator are allowed.
1. The likelihood for X = (X1 , . . .