The classical approach to actuarial problems has been deterministic. That is, the assumption has been made that the number of policies in force is large, that chance fluctuations are unimportant, and that the use of mean values is adequate. The actual cost to a company of an annuity, for example, may in fact vary from nothing (if the annuitant dies immediately) to a large amount (if he lives to be a nonogenarian). On average, the cost will be ax, and for many purposes, this value is good enough.