1.In this problem and the next one, we’re going to make a very simple spam checker program by just looking
ooking at how likely a given email is to be spam based on the words it contains. In particular, in this problem we’re going to count how often words are present in spam emails within some set of training data (which here means a set of emails that have already been marked as spam or not spam manually).
We have already started to write a function spam_score(spam_file, not_file, word), which takes in two filenames, along with a target word (a lowercase string). Both filenames refer to text files which must be in the same directory as hw07.py (we’ve provided several such files in hw07files.zip). The text files contain one email per line (really just the subject line to keep things simple) - you can assume that these emails will be a series of words separated by spaces with no punctuation. The first file contains emails that have been identified as spam, the second contains emails that have been identified as not spam.
Since you haven’t learned File I/O yet, we’ve provided code that opens the two files and puts the data into two lists of strings (where each element is one line - that is, one email). You then must complete the function, so that it returns the spam score for the target word. The spam score is an integer representing the total number of times the target word occurs across all the spam emails, minus the total number of times the word occurs in not-spam emails. Convert all words to lowercase before counting, to ensure capitalization does not throw off the count.
2.It is estimated that during any one hour period, an average of 10 Internet users visit the
website of Sport-Equip Ltd,
of Sport-Equip Ltd, a company that sells sports equipment. Some of the users
who visit the website end up buying sports equipment from the website while others are
simply browsing in order to obtain product information.
(a) Clearly explain and justify which probability distribution you would use to
describe the number of Internet users who visit the website of Sport-Equip Ltd
in a one hour period. [There is no need to calculate any probabilities for this part
of the question]
(b) What is the probability that during any half-hour period, there will be less than 3
visitors to the website?
(c) What is the probability that during any two-hour period, there will be more than
15 visitors to the website?
(d) If a user has just visited the website, find the probability that the website will
have another visitor within the next 10 minutes. In your answer, state the
probability distribution you have used and explain your choice.
(e) It is estimated that 40% of Internet users who visit Sport-Equip Ltd’s website
buy a product from the company. If 100 users visit the website over a given
period of time, find the probability that more than 50 of them will buy a product
from the company. In your answer, state the probability distribution you have
used and explain your choice
4.A lock can be opened by inputting the correct sequence of four digits in the correct order, regardless of the
ss of the previous inputs. If the lock has buttons representing the digits 0-9 then there are 10000 possible combinations from 0000-9999. In class, we indicated that no less than 10003 digits must be pressed to test every possible four digit sequence.
Is there a sequence of length 10003 that tests all possible combinations. If so, this sequence must be given to me in your write up as well as an explanation on how you came up with this sequence.
If there is no sequence of length 10003 that tests all possible combinations, can you come up a sequence with less than the maximum number (40000) which tests all possibilities? How did you come up with this sequence?
5.11. In a game, you draw thirteen cards with replacement from a deck of playing cards. If you draw any
y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?
6.1. Other than the Egyptian pyramids, what other pyramids does Akala discuss? 2. What Akala's address. Identify 2 facts discussed
. Identify 2 facts discussed at the beginning of the lecture (within the first 20-25 minutes) that you were unaware of prior to listening to his lecture. What does he say about these facts? Why are these facts significant? How might these facts impact American culture as well as African American culture? 3. What Akala's address. Identify 2 facts discussed at the end of the lecture (within the last 50 minutes to the end of the video) that you were unaware of prior to listening to his lecture. What does he say about these facts? Why are these facts significant? How might these facts impact American culture as well as African American culture? 4. Select 2 facts from Akala's address that you would like to know more about. Research the topic and write a 1-2 paged paper discussing what you learned. Tell why these facts interest you. How might these facts and what you learned impact you and AA culture? 5. Select 2 facts from Akala's address that you would like to know more about. Research the topic and write a 1-2 paged paper discussing what you learned. Tell why these facts interest you. How might these facts and what you learned impact you and AA culture? 6. Notice the audience members in attendance at Akala's speech given at Oxford. Use what you learned about the mis-education of a Negro to discuss what/who you see. Do you think Akala is mis-educated is some regards? Why or why not. 2-3 paragraphs
7.Wal-Mart has approached you with the opportunity to enter a sale lease-back transaction with them on a one million square
a one million square foot warehouse that they have recently developed. In typical Wal-Mart fashion, they have given you a “take it, or leave it” final offer. The terms are:
Purchase Price: $165 million
Facility Size 1,000,000 SF
Lease Term 7 years
Rent $7 PSF NNN
Operating Expenses Wal-Mart (tenant) pays all operating expenses, utilities, and property taxes (owner pays none)
Renewal Options 7-year extension at $8 per ft2; a second 7 year extension at $9.50 per ft 2; a third 7 year extension at $11.50 per ft.2. All at Wal-Mart’s choice (i.e. it’s Wal-Mart’s option). Wal-Mart pays all operating expenses, utilities, property taxes, and capital expenditures undertaken during all lease renewal periods.
You know the market and feel that the location is good, and that the warehouse market is in good supply/demand balance. Vacancy rates are 4% - 5% in quality facilities, while net rents in the market are running about $7.50 - $8 PSF (i.e. a slight premium to the Wal-Mart lease). You have recently seen comparable sales that have traded in the range of $160 - $200 PSF. You also know that implied discount rates are currently at about a 3% premium to implied cap rates and capital costs are running at $0.50 PSF per annum.
You know from your Real Estate Finance & Investments classes that you can value a building using a direct capitalization approach, a comps analysis and a DCF analysis. You also have a handy template that you’ve been using for these analyses which you will need to complete in order to come to a view on value.
It’s decision time…would you agree to pay the $165 million that Wal-Mart is asking? Why or why not?
8.The unit price of market goods is $1. Each person has 8 hours to work each day.
Another couple, Sylvan and
van and Alex, have the same productivities: Sylvan is identical to Rajan, while Alex
and Esther are identical.
Esther and Rajan both engage in market work. Sylvan works full time at home, so only Alex works in the
a) Given this information, which couple has the higher opportunity cost of home produced goods?
Explain how you determined this. You can add a diagram if that helps, but you are not required
to include one.
b) Can you determine which couple has the higher utility? Explain why or why not.
Suppose now that value of market production for both Alex and Esther increased to $12/per hour.
c) Explain the change in the household joint production possibility frontier generated by this
d) Explain what would happen to each couple’s choice of both household and market produced
goods, using an analysis by means of income and substitution effects.
e) What changes in time allocation for each couple that would be necessary to produce and
consume this new bundle? Briefly explain your reasoning.