Applied calculus on-line chapter: calculus applied to probability and statistics |

You are a financial planning consultant at a neighborhood bank. A 22-year-old client asks you the following question: "I would like to set up my own insurance policy by opening a trust account into which I can make monthly payments starting now, so that upon my death or my ninety-fifth birthday - whichever comes sooner - the trust can be expected to be worth $500,000. How much should I invest each month?" Assuming a 5% rate of return on investments, how should you respond?

To answer the question, we must know something about the probability of the client's dying at various ages. There are so many possible ages to consider (particularly since we should consider the possibilities month by month) that it would be easier to treat his age at death as a continuous variable, one that can take on any real value (between 22 and 95 in this case). The mathematics needed to do probability and statistics with continuous variables is calculus.

The material on statistics in this resource will be readily accessible to you if you are familar with derivatives and integrals (through Chapter 6 of *Applied Calculus*) and have a "common-sense" knowledge of probability. It also supplements any previous study you may have made of probability and statistics without using calculus.

The authors, Stefan Waner and Steven R. Costenoble, of the text on which this Web resource is based, are extremely grateful to the many reviewers who read earlier drafts of this material. We would welcome comments and suggestions for improving this resource further.

*Last Updated: January 2008
Web Version Copyright © 2008 Stefan Waner*