Why is the Sum of Independent Normal Random Variables Normal?
” Bennett Eisenberg and Rosemary Sullivan The fact that the sum of independent normal random variables is normal is fundamental in probability and statistics. The standard proofs using convolutions and moment generating functions do not give much insight into why this is true. This paper gives two more proofs, one geometric and one algebraic, that provide more insight into why the sum of independent normal random variables must be normal. A Converse to a Theorem on Linear Fractional Transformations Xia Hua An interesting geometric fact about a linear fractional transformation (also called Möbius transformation and bilinear transformation) is that it maps circles and lines to circles and lines in a bijective fashion. Naturally we want to ask: what can we say about an arbitrary bijective function that maps circles and lines onto circles and lines? We will show that any such function is either a linear fractional transformation or the complex conjugate of a linear fractional transformatio
