Actuary Certification ACTUARY Mathematics and Statistics 2

Question 1

A random variable X follows a Poisson distribution with mean λ = 4. What is P(X = 2)?

Accepted Answer

0.1465

Answer

P(X=2) = e^(-4) * 4^2 / 2! = e^(-4) * 8 ≈ 0.1465.

Question 2

Which of the following is the correct formula for the variance of a binomial distribution with parameters n and p?

Accepted Answer

np(1-p)

Answer

The variance of a binomial distribution is np(1-p), where n is the number of trials and p is the success probability.

Question 3

If X and Y are independent random variables with Var(X) = 5 and Var(Y) = 3, what is Var(2X - Y + 7)?

Accepted Answer

23

Answer

Var(2X - Y + 7) = 4·Var(X) + Var(Y) = 4(5) + 3 = 23; constants have zero variance.

Question 4

The moment generating function of a standard normal distribution is:

Accepted Answer

e^(t²/2)

Answer

For Z ~ N(0,1), the MGF is M(t) = e^(t²/2).

Question 5

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)?

Accepted Answer

38

Answer

SSE = SST(1 - R²) = 200(1 - 0.81) = 200(0.19) = 38.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification ACTUARY Mathematics and Statistics 2