Can I Start Studying Probability and Statistics After Algebra $1$, Geometry, Algebra $2$, and Linear Algebra?

Question

I have a question regarding my mathematical background and its readiness for studying Probability and Statistics. I have completed Algebra $1$, Geometry, Algebra $2$, and Linear Algebra (half done).

After completing Linear Algebra, I want to dive into Probability and Statistics (skipping calculus for now). However, I am uncertain whether my current foundation is sufficient to grasp the concepts presented in Probability and Statistics.

Please advise me on whether I am adequately prepared to begin studying Probability and Statistics at this stage? Should I expect to encounter any significant challenges due to my background? Or should I start calculus first then Probability and Statistics?.

The book I choose for Probability and Statistics are:

Probability and Statistics by Morris H. DeGroot, Mark J. Schervish https://www.amazon.com/Probability-Statistics-4th-Morris-DeGroot/dp/0321500466

Introduction to Probability and Statistics by William Mendenhall, Robert J. Beaver, Barbara M. Beaver https://www.amazon.com/Introduction-Probability-Statistics-William-Mendenhall/dp/1133103758

Recommendations for resources for Probability and Statistics would be appreciated.

Answer 1

You can "probably"(pun intended) search for some motivation for probability and statistics. A big chunk of probability is to study continuous distributions as many simple real world events can be modelled using them (eg normal distribution for height/weight distributions and many many other things, exponential distributions for decay of particles etc). If you don't know calculus, then you don't know integration(Newton/Leibnitz) and without this, you cannot make sense of a single thing in continuous distributions. Rules of Integration are a must to study the most basic and useful distributions.

More rigorously speaking, probability is a "measure" and the biggest advantage of measure theory is that we have a notion of integrals in "a" most general sense. So to understand Lebesgue integrals, you need to first study usual high school(or college level maybe in your country) calculus, then learn Riemann Integration and then learn Lebesgue Integrals. That's atleast two years worth of courses. But this is for people who want to get into it's depths and these really are graduate level concepts.

However, to get the intuition and do basic probability and statistics with good intuitive understanding, it suffices to learn high school level calculus (by which I mean precalculus,functions, limits, continuity, differentiability, differentiation, Integration and Multivariate calculus including notion of Jacobians and multiple integrals and change of variable rules and if it helps a basic understanding of Oridinary Differential equations which are taught in physics any way I guess). So strictly speaking, you can even ignore/skip a formal course in linear algebra and study probability. But, for me, skipping calculus and studying probability is not possible.

Bubba correctly points out that many social science and sociology students have to learn statistics but I'll be very blunt and directly say that those maybe enough for "art" students but not for "science/STEM" students if you are one.

If you are very new to calculus, then I will say that it'll take time to be proficient in it, especially integration, as there are a lot of rules and you have to develop a sixth sense of recognizing patterns and what method/step will bear fruits. That requires lots and lots of practice.

So, all in all, good luck and I hope this answer helps you.

Answer 2

I would highly reccommend learning a fair amount of calculus first. You might be able to intuitively grasp something like a probability density function, but some functions that are of incredible importance in statistics (notably the cdf of the standard distribution) can only be expressed in their integral form. It's therefore quite useful to know what integrals are, what they represent and to a certain degree how to calculate them.

Answer 3

For several years, I taught elementary probability & statistics to social sciences students who had pretty weak math backgrounds. I expect many other people have done the same. They knew basic algebra, but not linear algebra or calculus, and they’d certainly never heard of measure theory.

It can work, at some level. You can focus on discrete variables much of the time, and talk about areas under curves, rather than integrals, and so on.

If you’re self-studying, you just have to choose the right book. Maybe something like this, or this, for example. The Mendenhall book you mentioned doesn’t require any calculus.