ISYE 6644 MIDTERM SIMULATION EXAM
COMPLETE QUESTIONS AND DETAILED SOLUTIONS
LATEST UPDATE THIS YEAR JUST RELEASED
Question 1: Which of the following is not an integration method
discussed in this lesson?
A. Reimann Sums
B. Newmann Sums
C. Trapezoid Rule
D. The Monte Carlo method
Answer:
B) Newmann Sums
Question 2: What is the conditional probability of A given B?
Answer:
The probability of some event A, given event B, is equal to the probability of
the intersection of the two events A and B divided by the probability of B all by
itself.
Question 3: Regarding probability, events are independent when
what definition is met?
Answer:
If the probability of A intersect B equals P of a times P of B then A and B are
independent events.
Question 4: Toss a 4-side die twice (you know, one of those goofy
Dungeons and Dragons pyramid dice things). Assuming the die is
numbered 1,2,3,4, what's the probability that the sum will equal 3?
, A. 0
B. 1/2
C. 13/16
D. 1/8
Answer:
D) 1/8
Question 5: P(sum=3)=P((1,2)or(2,1))=P(1,2)+P(2,1)=2(1/16)=1/8.
TRUE or FALSE? f(x)=3e−xforx>0 is a legitimate probability density
function.
Answer:
FALSE
Question 6: Correct: In order to be a legit p.d.f., f(x) must integrate
to 1; but lo and behold. . .∫Rf(x)dx=∫∞03e−xdx=3.■ Suppose X is a
continuous random variable with cumulative distribution function
F(x). What is the distribution of the nasty random variable F(X)?
A. Normal
B. Unif (0,1)
C. Exponential
D. Weibull
Answer:
Unif (0, 1) - this is the Inverse Transform Theorem
Question 7: Suppose U is a Unif (0,1) random variable. Name the
distribution of X=−■n(1−U).
A. Normal
B. Unif (0, 1)
, C. Exponential
D. Weibull
Answer:
C) Exponential
Question 8: The abbreviation "m.g.f." stands for...
Answer:
Moment Generating Function
Question 9: What is the concept of double expectation?
Answer:
Idea: the average expected value of all of the conditional expected values is
the overall population average.
Question 10: TRUE or FALSE? If ■ and ■ are uncorrelated, then
they're independent.
Answer:
False
Question 11: What is the most-important theorem in the universe?
Answer:
Central limit theorem
Question 12: What is the central limits theorem?
Answer:
COMPLETE QUESTIONS AND DETAILED SOLUTIONS
LATEST UPDATE THIS YEAR JUST RELEASED
Question 1: Which of the following is not an integration method
discussed in this lesson?
A. Reimann Sums
B. Newmann Sums
C. Trapezoid Rule
D. The Monte Carlo method
Answer:
B) Newmann Sums
Question 2: What is the conditional probability of A given B?
Answer:
The probability of some event A, given event B, is equal to the probability of
the intersection of the two events A and B divided by the probability of B all by
itself.
Question 3: Regarding probability, events are independent when
what definition is met?
Answer:
If the probability of A intersect B equals P of a times P of B then A and B are
independent events.
Question 4: Toss a 4-side die twice (you know, one of those goofy
Dungeons and Dragons pyramid dice things). Assuming the die is
numbered 1,2,3,4, what's the probability that the sum will equal 3?
, A. 0
B. 1/2
C. 13/16
D. 1/8
Answer:
D) 1/8
Question 5: P(sum=3)=P((1,2)or(2,1))=P(1,2)+P(2,1)=2(1/16)=1/8.
TRUE or FALSE? f(x)=3e−xforx>0 is a legitimate probability density
function.
Answer:
FALSE
Question 6: Correct: In order to be a legit p.d.f., f(x) must integrate
to 1; but lo and behold. . .∫Rf(x)dx=∫∞03e−xdx=3.■ Suppose X is a
continuous random variable with cumulative distribution function
F(x). What is the distribution of the nasty random variable F(X)?
A. Normal
B. Unif (0,1)
C. Exponential
D. Weibull
Answer:
Unif (0, 1) - this is the Inverse Transform Theorem
Question 7: Suppose U is a Unif (0,1) random variable. Name the
distribution of X=−■n(1−U).
A. Normal
B. Unif (0, 1)
, C. Exponential
D. Weibull
Answer:
C) Exponential
Question 8: The abbreviation "m.g.f." stands for...
Answer:
Moment Generating Function
Question 9: What is the concept of double expectation?
Answer:
Idea: the average expected value of all of the conditional expected values is
the overall population average.
Question 10: TRUE or FALSE? If ■ and ■ are uncorrelated, then
they're independent.
Answer:
False
Question 11: What is the most-important theorem in the universe?
Answer:
Central limit theorem
Question 12: What is the central limits theorem?
Answer:
