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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.

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    $\begingroup$ From the Amazon link you provided, "Calculus is assumed as a prerequisite" already answered your question. $\endgroup$
    – Nobody
    Commented Aug 14, 2023 at 9:19

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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.

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  • $\begingroup$ @Henry you're absolutely right, I've edited my answer. Monday mornings, eh? :P $\endgroup$
    – simeondermaats
    Commented Aug 14, 2023 at 9:17
  • $\begingroup$ its a long road then, so i have to study cal 1, cal 2 and 3 first? $\endgroup$
    – Askani
    Commented Aug 14, 2023 at 9:24
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    $\begingroup$ @Askani I think Calc I and II should suffice; that being said I am not based in the US and I've only just skimmed through the curriculum. Calc II is more or less equivalent to sixth-form calculus here in Belgium and I got by perfectly fine. $\endgroup$
    – simeondermaats
    Commented Aug 14, 2023 at 9:30
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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.

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  • $\begingroup$ Thank you. I am new to calculus and am self-studying mathematics during my free time. $\endgroup$
    – Askani
    Commented Aug 14, 2023 at 10:21
  • $\begingroup$ That should suffice imo. Just solve as many as you can. There are also many youtube channels with content focussed on calculus. I would recommend an Indian book which the JEE advanced students use to learn. It's by G.Tewani Calculus for JEE Advanced. It's a very very comprehensive book. And for the multivariate part, to get a very basic but sufficiently intuitive understanding, the book by Murray Speigel's Vector Analysis. After you learn these two you can go into probability and develop a solid intuitive understanding. @Askani $\endgroup$
    – Mr.Gandalf Sauron
    Commented Aug 14, 2023 at 10:31
  • $\begingroup$ @Mr.GandalfSauron. I don’t think many people would consider psychology, sociology, environmental studies etc to be “art”. $\endgroup$
    – bubba
    Commented Aug 15, 2023 at 7:21
  • $\begingroup$ @bubba I don't know about the US, but in most countries, if you graduate from any of the streams you mentioned above, you do get a Bachelor of Arts degree and not a BSc or BS degree. Okay, you might consider that to be a moot point as math graduates are sometimes given a BA degree. Psychiatry is a science and also requires you to get a MD degree to be a practitioner. Psychology is an arts subject and so is social science and environmental studies as far as my country(India) is concerned. I have to say that I prefer that these be categorized as arts subjects and not science. $\endgroup$
    – Mr.Gandalf Sauron
    Commented Aug 15, 2023 at 7:36
  • $\begingroup$ The reason for my preference(limited to my country) is that most students who pursue these actually don't want to enter the science stream(here you have to make a choice at the high school level if you want to be a science student or an arts or commerce student). Sometimes these choices are explicitly determined by one's fear/hatred towards maths and frankly speaking, I won't like people to call themselves a scientist if they hate maths. Ofcourse there are exceptions but again, as far as India is concerned that is only just a few hundred in a such a large population. @bubba $\endgroup$
    – Mr.Gandalf Sauron
    Commented Aug 15, 2023 at 7:45
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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.

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In my own experience, mainly because of how things are done at my school, I think you should be able to take Probability and Statistics. But it ultimately depends on your school's curriculum. (I spell that right?) My school allows you to take Probability and Statistics after completing specifically Algebra 1, but it can easily be different with other schools.

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