ACTUARY Mathematics and Statistics Flashcards
7 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 ACTUARY Mathematics and Statistics flashcards as text
A random variable X follows a Poisson distribution with mean λ = 4. What is P(X = 2)?
Answer: 0.1465
P(X=2) = e^(-4) * 4^2 / 2! = e^(-4) * 8 ≈ 0.1465.
Which of the following is the correct formula for the variance of a binomial distribution with parameters n and p?
Answer: np(1-p)
The variance of a binomial distribution is np(1-p), where n is the number of trials and p is the success probability.
If X and Y are independent random variables with Var(X) = 5 and Var(Y) = 3, what is Var(2X - Y + 7)?
Answer: 23
Var(2X - Y + 7) = 4·Var(X) + Var(Y) = 4(5) + 3 = 23; constants have zero variance.
The moment generating function of a standard normal distribution is:
Answer: e^(t²/2)
For Z ~ N(0,1), the MGF is M(t) = e^(t²/2).
An actuary fits a linear regression model Y = β₀ + β₁X + ε. The coefficient of determination R² = 0.81 and SST = 200. What is SSE (sum of squared errors)?
Answer: 38
SSE = SST(1 - R²) = 200(1 - 0.81) = 200(0.19) = 38.
For a continuous uniform distribution on [a, b], what is the variance?
Answer: (b-a)²/12
The variance of U(a,b) is (b-a)²/12.
If the joint density of (X,Y) is f(x,y) = 2 for 0 < x < y < 1, what is the marginal density of Y?
Answer: 2y
f_Y(y) = ∫₀ʸ 2 dx = 2y for 0 < y < 1.