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| Section | Objectives |
|---|---|
| Probability and Statistics | - Probability theory - Descriptive statistics - Statistical distributions |
| Mathematical Techniques | - Basic modeling concepts - Mathematical notation and functions |
| Fundamental Mathematics | - Algebra
|
Question 1
Let a and b be two positive numbers and let m and n be two positive integers.
Identify which of the followingequalities is false.
A)
B)
C)
D)
A. Option A
B. Option B
C. Option C
D. Option D
Question 2
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 B
C. Option C
D. Option D
Question 3
Identify which of the following statements is correct.
A. is equal to x.
B. can be greater than or less than x.
C. is less than x
D. is greater than x
Question 4
Calculate the single extreme point of the function:
A. (0.1)
B. (1.1)
C. (0,4)
D. (0,2)
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: D | Question 2 Answer: D | Question 3 Answer: A | Question 4 Answer: D | Question 5 Answer: D |
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