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Course Notes for Math 162: Mathematical Statistics
The Cram¶er-Rao Inequality
Adam Merberg and Steven J. Miller

Contents
1 Description of the Problem 1
2 The Cram¶er-Rao Inequality 2
3 Examples and Exercises 5
A Interchanging Integration and Di®erentiation 7
B The Cauchy-Schwarz Inequality 8
C The Exponential Density 9
D When the Cram¶er-Rao Inequality Provides No Information 9