Samples from Normal Distributions

The main goal of this chapter is to obtain the result at the end of section 6.3 which is part of the basis for the initialization of annealing as described in section 8.1. On the way to this result we formally define some density functions that are going to be used in chapter 7. After all this effort to obtain theorem 6.14 it is only a small step to the special case of the central limit theorem of section 6.4. This chapter is therefore the background of much that is in chapter 7 and the proof of theorem 8.2. The presentation there is such that it can be read without going through the details of this chapter. These results are achieved by using the characteristic function of a random variable. In section 6.1 this function is defined and some of its more important properties are derived.