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| Section | Weight | Objectives |
|---|---|---|
| Financial Mathematics Basics | 20% | - Time value of money - Interest rates and discounting - Annuities and perpetuities - Basic investment and cash flow concepts |
| Introduction to Actuarial Concepts | 10% | - Basic actuarial applications - Overview of actuarial work and risk management |
| Probability and Statistics | 40% | - Basic probability theory - Discrete and continuous probability distributions - Measures of location, dispersion and correlation - Statistical inference and hypothesis testing - Data presentation and analysis |
| Fundamental Mathematics | 30% | - Algebra, equations and inequalities - Differential and integral calculus - Mathematical constants and standard functions - Sequences and series - Numerical methods |
Question 1
Let X and Y be two independent random variables.
Identify which of the following statements is false.
A. E[X2] = E[X]E[X]
B. E[X-Y] =E [X] - E [Y]
C. E [XY] E [X] E [Y]
D. E[2X] = 2E [X
Question 2
The distribution of test scores from a recent clinical drug study have been tabulated below.
Determine i) whether the distribution of test scores are symmetric positively skewed or negatively skewed, and ii) the sample median value.
A. i) Positively skewed, ii) 3
B. i) Negatively skewed, ii) 3
C. i) Positively skewed, ii)
D. i) Symmetric, ii) 4
Question 3
Determine the binomial expansion of (2x-X2)3.
A. -x6+2x5-4x4+8x3
B. -x8+2xa-4x4+8x3
C. -x6+3x5-3x4+x3
D. -X6+8x3
Question 4
Two real numbers, x and y, satisfy the following inequalities:
Determine which statement is true.
A. y cannot be zero.
B. y must be positive.
C. y can be negative.
D. y cannot be negative.
Question 5
Let X be a continuous random variable with probability density function f(x) that is defined over all real numbers.
DefineE[g(X)]whereg(x)is a continuous function.
A)
B)
C)
D)
A. Option
B. Option
C. Option
D. Option
Solutions:
| Question 1 Answer: A | Question 2 Answer: A | Question 3 Answer: A | Question 4 Answer: D | Question 5 Answer: D |
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