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CAA Global Entry exam of the Certified Actuarial Analyst qualification Sample Questions:

1. Identify which of the following statements is correct.
A continuous random variable is one that:

A) can take one of a finite number of values
B) can take one of an infinite number of values.
C) can only take positive values.
D) must be approximated using a discrete random variable.

2. A set of 17 observed values is being studied.
Identify which of the following statements is/are true.
I The median must be equalto one of the observed values.
II. The mean could be different from all of the observed values.
Ill If the observations are positively skewed, then the mean is less than the median IV. More than one mode is not possible.

A) III only
B) I and II only
C) II and IV only
D) I only

3. Determine the stationary point(s) for the following function

A) Maximum at x = 1 and maximum at x = 3.
B) Minimum at x = -1 and maximum at x = -3.
C) Minimum at x = 1 and minimum at x = 3.
D) Minimum at x = -3 and maximum at x = -1.

4. 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 second derivative of the function with respect to x takes the value 2, 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 value of the function at x = 3 is 11, which is positive.

5. The volume of a cone can be determined by summing up the infinitesimal circular cross-sections of the cone across the length of the cone Consider the function f(x) = x2 for x contained in [0,1].

Now consider an infinitesimal circular cross-sectional element of width dx and radius r = f(x) Determine the volume of the cone enclosedby the function f(x) by considering the volume of each circular cross-sectional element (Recall thatthe sum of infinitesimal elements can be represented as an integral Recall also that the area of a

circle is
A)

B)

C)

D)
1

A) Option A
B) Option D
C) Option C
D) Option B

Solutions: