# References for probability using Calculus

I have to teach a Calculus class (details on the syllabus below) and I want to add some applications to other sciences. But I would like to avoid the classical physics examples, because the physics teacher will be way better than I am to explain beautiful physics. So I decided to try to teach some probabilities (with maybe some statistics) to my students to keep them motivated.

For example, the computation of the mean of a geometric distribution involves the computation of a series.

Unfortunately, the only references I know for probabilities use Lebesgue integrals. Do you have any recommandations for a probability book which would use only Calculus materials (beside the usual combinatorics materials) and no deep analysis tools? Basically, something for University 1st or 2nd year or engineer major?

Syllabus: what my students know or will learn during this course (roughly Chapter 1 to 11 of Stewart's Calucus): continuity, derivatives and integrals; applications of integrals (volume, arclength,...); basics on parametric curves and polar curves; methods 1st and 2nd order differential equations; series and power series.

PS: books would preferably be in English but Spanish or French is also acceptable.

## 2 Answers

I found "Engineering and Statistics or Engineering and the Sciences" by Jay Devore to be a useful calculus based intro without the measure theory. Also, a great way to show the utility of calculus and probability is Maximum Likelihood Estimation...its a very direct application of calculus to a probability model, and its used to compute estimates for data (and is in very common use) so it will feel very germane to your students.

I think Hoel's Introduction to Probability Theory is right on the spot for you. It doesn't require advanced math, it is slim (but not without explanations), it has answers for all its exercises (which aren't overly difficult) and has plenty of them.