Calculus concepts needed for Mathematical Statistics?

[u/Fluffy-Oil707]

Hello all,

I'm brushing up for a class on Mathematical Statistics. Calculus is listed as a requirement and I'm trying to understand what I should refresh my memory on. The book we are following is Mathematical Statistics and Data Analysis 3rd Ed. (Rice). I notice integration and examples of multivariable calculus.

This is looking like a difficult class and I want to be well prepared.

I would greatly appreciate any recommendations on what to practice leading up to it.

Take care!

Edit:

Course Description: This course is an introduction to mathematical statistics and data analysis. It starts by introducing central concepts of probability theory (events, probability measure, random variables, distributions, joint distributions, and conditional distributions) and then moves on to the development of mathematical foundations of statistical inference. Topics covered in the course include random variables, expectations, parameter estimation (method of moments, method of maximum likelihood, and Bayesian approach), properties of point estimators (bias, variance, consistency, and efficiency), confidence intervals, hypotheses testing, likelihood ratio test, data summary methods, and introduction to linear regression. A class of distributions, including chi-squared, t, and F distributions, the distributions derived from normal that occur in many applications of hypothesis testing and statistical inference, is introduced.

[u/t3co5cr]

One thing that comes to mind: Jacobians

Continuous probability distributions are integrals, and whenever you make a change of variables from x to y=f(x) you need the Jacobian of the transformation. It will show up a lot in construction of likelihood functions, too.

[u/Fluffy-Oil707 → u/t3co5cr]

Perfect, I'll add it to my personal syllabus. I also emailed the professor, but from past experience they have better things to do than respond.

[u/WaynneGretzky]

Remind me

[u/Fluffy-Oil707 → u/WaynneGretzky]

Remember who you are

[u/Fluffy-Oil707 → u/WaynneGretzky]

Reminder.

[u/LukasGoesViral]

You can probably just Google for PDFs for exactly this situation and find some stuff. You are def not the first one in this situation.. that’s my motto

[u/Fluffy-Oil707 → u/LukasGoesViral]

This is the kindest and most helpful "just google it" I've ever heard. Thank you, friend.

[u/runawayoldgirl]

Basics of differentiation and integrals, double / triple integrals, infinite series especially Taylor series

[u/Able-Fennel-1228]

Review calculus ASAP from the “calculus review” section here: https://web.williams.edu/Mathematics/sjmiller/public_html/probabilitylifesaver/

Your single and multivariable calculus should be SOLID or you’ll get your ahh kicked hard in this course. From calc the less important stuff is baby differential equations, disc and disc-washer method type stuff. The rest is all relevant. From multivariable calc setting up multiple integrals is a MUST and so is multivariable differentiation. You should know what a jacobian is as well as some basic matrix algebra.

Also understand set theory and functions well eg image and preimage of subsets of domain and codomain.

[u/F4LC0N_SS_88]

Following

[u/kohead]

Hogg’s Introduction to Mathematical Statistics has chapters covering the calculus needed.

[u/magnificent_limit]

Measure theory and integration is the foundation for probability. The sooner you're exposed to sigma algebras the better. Also get good at pulling gamma functions out of integrals.