Entry exam of the Certified Actuarial Analyst qualification

Question 1

Identify which of the following statements is correct.
For a continuous random variable X, the distribution function evaluated at X= x measures:

A. P(X = x)

B. P(X<x)

C. P(X>x)

D. P(xx)

Correct Answer: B

Question 2

Consider the function f(x)x2 6x=20. This functions has a stationary point at x=3.
Determine the nature of this stationary point and how we know this to be true.

A. It is a maximum stationary point because the value of the function at x = 3 is 11, which is positive.

B. It is a minimum stationary point because the value of the function at x = 3 is 11, which is positive.

C. It is a minimum stationary point because the second derivative of the function with respect to x takes the value 2 which is positive.

D. It is a maximum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.

Correct Answer: B

Question 3

Calculate the determinant of the product of the matrices given below:

A. -78

B. -60

C. -440

D. -0 00227

Correct Answer: C

Question 4

Differentiate with respect to X:

A)

B)

C)

D)

A. Option D

B. Option B

C. Option A

D. Option C

Correct Answer: D

Question 5

In an Olympic Race there are 100 competitors.
Calculate the number of ways of distributing the Gold. Silver and Bronze medals amongst all of the competitors.
A)