Are you preparing for the Society of Actuaries (SOA) Exam P? This comprehensive cheat sheet covers all the essential concepts you need to master. Bookmark this page and use it as your quick reference guide while studying!
Contents
Key Information About Exam P
The SOA Exam P tests your knowledge of probability concepts. Here’s what you need to know:
- Duration: 3 hours
- Number of questions: 30 multiple-choice questions
- Passing score: Typically around 70% (varies by sitting)
- Calculator: Only BA-II Plus or BA-II Plus Professional allowed
Essential Probability Concepts
Basic Probability Rules
Addition Rule:
For any two events A and B:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Multiplication Rule:
For dependent events:
P(A ∩ B) = P(A) × P(B|A)
For independent events:
P(A ∩ B) = P(A) × P(B)
Conditional Probability
The formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Bayes’ Theorem
The fundamental formula:
P(A|B) = [P(B|A) × P(A)] / P(B)
Extended form:
P(Ai|B) = [P(B|Ai) × P(Ai)] / Σ[P(B|Aj) × P(Aj)]
Random Variables
Types of Random Variables
- Discrete Random Variables
- Takes on countable values
- Probability mass function (PMF): P(X = x)
- Cumulative distribution function (CDF): F(x) = P(X ≤ x)
- Continuous Random Variables
- Takes on any value in an interval
- Probability density function (PDF): f(x)
- CDF: F(x) = ∫[from -∞ to x] f(t)dt
Expected Value and Variance
Expected Value:
- Discrete: E(X) = Σ[x × P(X = x)]
- Continuous: E(X) = ∫[from -∞ to ∞] x × f(x)dx
Variance:
Var(X) = E(X²) – [E(X)]²
Common Distributions
Discrete Distributions
Binomial Distribution:
- Parameters: n (trials), p (probability of success)
- PMF: P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
where C(n,k) is the binomial coefficient - Mean: n × p
- Variance: n × p × (1-p)
Poisson Distribution:
- Parameter: λ (rate)
- PMF: P(X = k) = (e^(-λ) × λ^k) / k!
- Mean: λ
- Variance: λ
Continuous Distributions
Normal Distribution:
- Parameters: μ (mean), σ (standard deviation)
- PDF: f(x) = [1/(σ√(2π))] × e^(-(x-μ)²/(2σ²))
- Standard Normal: Use Z-table for Z = (X-μ)/σ
Exponential Distribution:
- Parameter: θ (mean)
- PDF: f(x) = (1/θ) × e^(-x/θ)
- Mean: θ
- Variance: θ²
Transformation Techniques
Moment Generating Functions (MGF)
The MGF is defined as:
M_X(t) = E(e^(tX))
Properties:
- Mean: E(X) = M’_X(0)
- Variance: Var(X) = M”_X(0) – [M’_X(0)]²
Study Tips
- Practice Time Management
- Spend no more than 6 minutes per question
- Learn to recognize when to skip difficult questions and return later
- Focus on Fundamentals
- Master basic probability rules before moving to complex topics
- Understand the relationships between distributions
- Practice deriving formulas rather than memorizing them
- Use Practice Exams
- Complete multiple practice exams under timed conditions
- Review mistakes thoroughly to understand where you went wrong
Exam Day Preparation
- Calculator Setup
- Clear your calculator’s memory
- Practice using all necessary functions
- Bring backup batteries
- Required Items
- Valid ID
- Admission ticket
- Approved calculator
- Arrive 30 minutes early
Final Words
Remember that success in Exam P comes from consistent practice and understanding concepts, not just memorization. Use this cheat sheet as a quick reference, but ensure you deeply understand each topic through practice problems and detailed study.
Good luck with your exam preparation!
