Introduction

We begin with what may be viewed as a small miracle. Two investors, Ann and Paul, expect random incomes amounting to random variables (r.v.’s) X1 and X2, respectively. We do not exclude the case when the X ’s may take negative values, which corresponds to losses. For simplicity, suppose X1 and X2 are independent with the same probability distribution. Then X1 and X2 have the same expected value m = E{Xi} and variance σ2 =Var{Xi}.