Week 1 Homework

.docx

School

Georgia Institute Of Technology *

*We aren’t endorsed by this school

Course

6242

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

11

Uploaded by BailiffNeutron10026 on coursehero.com

Week 1 Homework Due  Jan 19 at 8:59pm   Points  12   Questions  12   Available  Jan 12 at 5am - Jan 22 at 8:59pm   Time Limit  None Instructions Please answer all the questions below. This quiz was locked Jan 22 at 8:59pm. Attempt History Attempt Time Score LATEST Attempt 1 50 minutes 12 out of 12 Score for this quiz: 12 out of 12 Submitted Jan 12 at 8:51pm This attempt took 50 minutes.
Question 1 1 / 1 pts (Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height 0 = 1000 feet. You're a strong bloke, so the initial downward velocity is �0 = -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 (�)= 0+�0�−16�2 When does the rock hit the ground? a. -11.625 sec b. 2 sec Correct! c. 5.375 sec Set 0= (�)=1000−100�−16�2, and solve for t. Quadratics are easy: �=−�±�2−4��2�=100±1002+4(16)(1000)2(−16)=−100±272.032=5.375, which we take as the answer since the negative answer doesn't make practical sense. d. 11.625 sec e. 10 sec Set 0= (�)=1000−100�−16�2, and solve for t. Quadratics are easy: �=−�±�2−4��2�=100±1002+4(16) (1000)2(−16)=−100±272.032=5.375, which we take as the answer since the negative answer doesn't make practical sense.
Question 2 1 / 1 pts (Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is occupied, 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 as an M/M/1/1 queue. If �(�) denotes the probability that a customer is being served at time t, trust me that it can be shown that �(�)=��+�+[�(0)−��+�]�−(�+�)�. If the system is empty at time 0, i.e., �(0)=0, what is the probability that there will be no people in the system at time 1 hr? a. 1 b. 2/3 c. 0.397 Correct! d. 0.603 At time �=1, we have 1−�(�)=1−��+�−[�(0)−��+�]�−(�+�)�=��+�−[�(0)−��+�]�− (�+�)�=32+3−[0−25]�−(5)(1)=0.603 At time �=1, we have 1−�(�)=1−��+�−[�(0)−��+�]�−(�+�)�=��+�− [�(0)−��+�]�−(�+�)�=32+3−[0−25]�−(5)(1)=0.603 Question 3 1 / 1 pts (Lesson 1.4: History.) 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. Correct!
a. Merton Miller and William Sharpe for accomplishments in related (but slightly different) subject areas. b. Henry Kissinger c. Albert Einstein d. Subrahmanyan Chandrasekhar for accomplishments in related (but slightly different) subject areas. Question 4 1 / 1 pts (Lesson 1.5: Applications.) Which of the following situations might be good candidates to use simulation? (There may be more than one correct answer.) a. We put $5000 into a savings account paying 2% continuously compounded interest per year, and we are interested in determining the account's value in 5 years. Correct! b. 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. Correct! c. 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.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help