If you desire to become an actuary, then passing Exam P on Probability is your opportunity to enter the actuarial science profession and get a starting salary ranging of about $44,000 to $58,000 per year. But the colossal number of topics listed on the syllabus may seem intimidating to many. Fortunately, you do not need to know all of them to get high grades on the exam. I recently passed Exam 1P and can offer some advice on what you need to know in order to do well.
Of course, you need to know the basics of probability theory, including the addition and multiplication rules, mutually independent and dependent events, conditional probabilities, and Bayes’ Theorem. These topics are quite straightforward and do not require knowledge of calculus or any other kind of advanced mathematics; you need to be able to add, multiply, divide, and think logically about the situation presented in the problem — which will often be described in words. Visual aids, such as Venn Diagrams, contingency tables, and the use of union and intersection notation can be eminently helpful here. Try to master these general probability topics before moving on to the more difficult univariate and multivariate probability distributions.
Next, you will need to know several critically important univariate probability distributions, including some of their special properties. Fortunately, you do not need to know as many as the syllabus suggests.
The Society of Actuaries (SOA) recommends that you learn the “binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal, gamma, Weibull, and normal” distributions, but in fact the ones you will be tested on most extensively are just the binomial, negative binomial, geometric, Poisson, uniform, exponential, and normal. Make sure you know those seven in exhaustive detail, though, because much of the test concerns them. It is a good idea to memorize the formulas for these distributions’ probability density functions, survival functions, means, and variances. Also be able to do computations with the normal distribution using the provided table of areas under the normal curve. Knowledge of calculus, integration, and analysis of discrete finite and infinite sums is necessary to master the univariate probability distributions on Exam 1P.
Also pay attention to applications of univariate probability distributions to the insurance sector; know how to solve every kind of problem which involves deductibles and claim limits, because a significant portion of the problems on the test will employ these concepts. Study the SOA’s past exam questions and solutions and read the study note on “Risk and Insurance” to get extensive exposure to these applications of probability these.
The multivariate probability concepts on Exam 1P are among the most challenging. They require a solid grasp of double integrals and firm knowledge of joint, marginal, and conditional probability distributions — as well as the ability to derive any one of these kinds of distributions from the others. Moreover, many of the problems on the test involve moment generating functions and their properties — a subject that deserves extensive study and practice in its own right.
Furthermore, make sure that you have a solid grasp of the concepts of expectation, variance, standard deviation, covariance, and correlation. Indeed, try to master the problems involving variances and covariances of multiple random variables; these problems become easy once you make a habit of doing them; solving them quickly and effectively will save a lot of time on the exam and boost your grade. Also make sure that you study the Central Limit Theorem and are able to do problems involving it; this is not a difficult concept once you are conversant with the normal distribution, and mastering central limit problems can go a long way to enhance your performance as well.
Studying the topics mentioned here can focus your preparation for Exam 1P and enable you to practice effectively and confidently. Remember, though, that this is still a lot of material. You would be well advised to begin studying for the test at least three months in advance and to study consistently on a daily basis. Practice often with every kind of problem so as to keep your memory and skills fresh. Best wishes on the exam.