# Calculus Applied to Probability and Statistics for Liberal Arts and Business Majors

## A Complete Text Resource on the World Wide Web by Stefan Waner and Steven R. Costenoble

 1. Continuous Random Variables and Histograms Exercises 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta Exercises 3. Mean, Median, Variance and Standard Deviation Exercises 4. You're the Expert Creating a Family Trust Back to Main Page

Introduction

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 on the previous page, 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 Calculus Applied to the Real World or equivalent) 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 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.

Mail us at:
 Stefan Waner (matszw@hofstra.edu) Steven R. Costenoble (matsrc@hofstra.edu)
Last Updated: September, 1996