# Calculus in Statistics

1. Apr 10, 2012

### selig5560

Hi,

I know the title of this thread is very vague, so I apologize. How much calculus is actually used in statistics? I've heard Linear Algebra is one of the most used fields of math in statistics, but am interested in other opinions.

2. Apr 10, 2012

### chiro

Hey selig5560 and welcome to the forums.

Calculus is used quite extensively not only for calculating various probabilities for continuous distributions but also finding various optimization results that are used to minimize variances which help us find things like optimal estimators, optimal stratification and survey methodologies among other things.

The thing to realize is that whenever you have continuous distributions or you need to optimize something, calculus will be used.

The continuous distributions are many and include but are not limited to Normal, Exponential, Chi-Square, Student-T, Cauchy and Beta amongst many others. They all have different uses in different context. You also have the multivariable distributions like the Multivariate-Normal distribution and a massive range of other ones.

Also the Maximum Likelihood procedure uses calculus. The minimization of variance will often use things like Lagrange Multipliers for various things.

3. Apr 11, 2012

### camillio

Hi, I'd say that mostly basic calculus is a necessary prerequisite for basic statistics. By basic I mean differentiation and integrals. Usually, you do not need a deep knowledge of calculus, unless you plan to study statistics into high detail. The latter case, however, assumes at least a basic knowledge of measure and Lebesgue integration and probability theory etc. etc. etc.

In sum: learn basic differentiation and integration and you will be happy with it in most of the introductory statistics. If you start to like it, there will appear a lot of things to learn (and again, become happy :-))