ISYE 6644 QuizBank - 1 (2)Questions And Answers Rated
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Homework 1
Q (Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height h0= 1000 feet. You're a strong bloke, so the initial downward velocity
isv0 = -100 feet/sec (slightly under 70 miles/hr). Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is h ( t )=h + v t −16 t .When does the rock hit the ground?
2
0 0
c. 5.375 sec
TI89: solve(0 = 1000 – 100×t – 16t^2, t)
Q (Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between customer arrivals are independent, identically distributed
2 3
exp (λ= hr ) random variables; and the service times are i.i.d. exp
(µ= hr ) . Unfortunately, if a potential arriving customer sees that the server is occupied,
λ
he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at any time. This is what’s known λ
as an M/M/1/1−queue.
( λ+ μ ) t
If P(t) denotes the probability that a customer is being served at time t, trust me that it can be shown that P ( t )=
empty at time 0, i.e., P ( 0)=0, what is the probability that there will be no people in the system at time 1 hr?
λ+ μ [
+ P ( 0)−
λ+ μ ] e
If the system is
d. 0.603
TI 89: 1 - (2/5 + ( 0 - 2/5) * e^(-5))
Q Harry Markowitz (one of the big wheels in simulation language development) won his Nobel Prize for portfolio theory in 1990, though the work that earned
him the award was conducted much earlier in the 1950s. Who won the 1990 Prize with him? You are allowed to look this one up.
Merton Miller and William Sharpe
Q Which of the following situations might be good candidates to use simulation? (There may be more than one correct answer.)
We are interested in investing one half of our portfolio in fixed-interest U.S. bonds and the remaining half in a stock market equity index. We have some
information concerning the distribution of stock market returns, but we do not really know what will happen in the market with certainty.
We have a new strategy for baseball batting orders, and we would like to know if this strategy beats other commonly used batting orders (e.g., a fast guy bats
first, a big, strong guy bats fourth, etc.). We have information on the performance of the various team members, but there’s a lot of randomness in baseball.
Consider an assembly station in which parts arrive randomly, with independent exponential interarrival times. There is a single server who can process the
parts in a random amount of time that is normally distributed. Moreover, the server takes random breaks every once in a while. We would like to know how big
any line is likely to get.
Suppose we are interested in determining the number of doctors needed on Friday night at a local emergency room. We need to ensure that 90% of patients get
treatment within one hour.
Q The planet Glubnor has 50-day years. Suppose there are 2 Glubnorians in the room. What’s the probability that they’ll have the same birthday?
1/50
TI89: 1- nPr(50,2) / 50^2
Q The planet Glubnor has 50-day years. Now suppose there are 3 Glubnorians in the room. (They’re big, so the room is getting crowded.) What’s the probability
that at least two of them have the same birthday?
d. 0.0592
TI89: 1- nPr(50,3) / 50^3
Q (Lessons 1.6 and 1.7: Baby Examples.) Inscribe a circle in a unit square and toss n=500 random darts at the square. Suppose that 380 of those darts land in
A+ New Update Assured Satisfaction
Homework 1
Q (Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height h0= 1000 feet. You're a strong bloke, so the initial downward velocity
isv0 = -100 feet/sec (slightly under 70 miles/hr). Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is h ( t )=h + v t −16 t .When does the rock hit the ground?
2
0 0
c. 5.375 sec
TI89: solve(0 = 1000 – 100×t – 16t^2, t)
Q (Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between customer arrivals are independent, identically distributed
2 3
exp (λ= hr ) random variables; and the service times are i.i.d. exp
(µ= hr ) . Unfortunately, if a potential arriving customer sees that the server is occupied,
λ
he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at any time. This is what’s known λ
as an M/M/1/1−queue.
( λ+ μ ) t
If P(t) denotes the probability that a customer is being served at time t, trust me that it can be shown that P ( t )=
empty at time 0, i.e., P ( 0)=0, what is the probability that there will be no people in the system at time 1 hr?
λ+ μ [
+ P ( 0)−
λ+ μ ] e
If the system is
d. 0.603
TI 89: 1 - (2/5 + ( 0 - 2/5) * e^(-5))
Q Harry Markowitz (one of the big wheels in simulation language development) won his Nobel Prize for portfolio theory in 1990, though the work that earned
him the award was conducted much earlier in the 1950s. Who won the 1990 Prize with him? You are allowed to look this one up.
Merton Miller and William Sharpe
Q Which of the following situations might be good candidates to use simulation? (There may be more than one correct answer.)
We are interested in investing one half of our portfolio in fixed-interest U.S. bonds and the remaining half in a stock market equity index. We have some
information concerning the distribution of stock market returns, but we do not really know what will happen in the market with certainty.
We have a new strategy for baseball batting orders, and we would like to know if this strategy beats other commonly used batting orders (e.g., a fast guy bats
first, a big, strong guy bats fourth, etc.). We have information on the performance of the various team members, but there’s a lot of randomness in baseball.
Consider an assembly station in which parts arrive randomly, with independent exponential interarrival times. There is a single server who can process the
parts in a random amount of time that is normally distributed. Moreover, the server takes random breaks every once in a while. We would like to know how big
any line is likely to get.
Suppose we are interested in determining the number of doctors needed on Friday night at a local emergency room. We need to ensure that 90% of patients get
treatment within one hour.
Q The planet Glubnor has 50-day years. Suppose there are 2 Glubnorians in the room. What’s the probability that they’ll have the same birthday?
1/50
TI89: 1- nPr(50,2) / 50^2
Q The planet Glubnor has 50-day years. Now suppose there are 3 Glubnorians in the room. (They’re big, so the room is getting crowded.) What’s the probability
that at least two of them have the same birthday?
d. 0.0592
TI89: 1- nPr(50,3) / 50^3
Q (Lessons 1.6 and 1.7: Baby Examples.) Inscribe a circle in a unit square and toss n=500 random darts at the square. Suppose that 380 of those darts land in
