Appendix A

The Normal Density

There is a plethora of books on probability and statistics that cover the important normal distribution, and I recommend one among many excellent texts, the volume by Ross [99], especially Chapters 5, 6, and 7, where most of the elementary facts can be found.

Recall that a continuous random variable *X* is normally distributed with parameters *μ* and *σ* if its density function is defined, for all i, by

(A.1)

It is known that E(*X*) = *μ* and Var(*X*) = *σ*^{2}. Suppose we have *n* independent samples *X*_{1}, *X*_{2}, . . . , *X _{n}* from a normal distribution having an unknown mean that is now designated as

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