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

0.0916

Answer

0.1954

Answer

0.2381

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

np

Answer

np²

Answer

n²p(1-p)

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

11

Answer

17

Answer

27

Question 4

The moment generating function of a standard normal distribution is:

Accepted Answer

e^(t²/2)

Answer

e^t

Answer

e^(μt + σ²t²/2)

Answer

1/(1-t)

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

162

Answer

200

Answer

242

Question 6

For a continuous uniform distribution on [a, b], what is the variance?

Accepted Answer

(b-a)²/12

Answer

(b-a)/2

Answer

(b-a)²/4

Answer

(b-a)/12

Question 7

If the joint density of (X,Y) is f(x,y) = 2 for 0 < x < y < 1, what is the marginal density of Y?

Accepted Answer

2y

Answer

2(1-y)

Answer

1

Answer

2y(1-y)

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