Statistics help needed

Deep Learning Unit Two

1 Directions

STEP 1:

Print the entire document out and before you start print out your name on the

assignment, you may laugh at this instruction but I cannot begin to tell you the

number of times that I have had this happen on tests

STEP 2:

Answer the questions as fully as you can, showing as much work as you think is

necessary, if you are using a calculator you must let me know by stating ’used

calculator here’ and then stating what command(s) you used to get the calcu-

lator to do what you needed it to do.

STEP 3:

Scan this as a PDF, for those of you without a scanner handy you can us any

smart phone app ”pic to PDF” converter to create a PDF. Make sure to do this

in a reasonable quality so that it is legible.

STEP 4:

Upload your PDF into CANVAS

Note: As this is the first time I am using these assignments I will be ”nicer” with the grading than I might normally be. For bonus points I would love to here from you with feed back on what worked and what didn’t work with this assignment :)

1

2 Problem Set

Please answer the following as clearly as possible in the space pro- vided for the problem. A good rule of thumb is that if your instructor has to hunt for your work or the solution you probably won’t get the maximum credit available.

1. A certain Deli that I know of wants to get more repeat cus- tomers and has the great idea that all of its sandwiches should be named. Using the above copy of their deli-sandwich order ticket find the total number of unique sandwiches that can be named.

There will be a few ”good” ways to count this out so for full credit you must provide your reasoning as best that you can. Points will be awarded for good thinking process not on coming up with the one true answer.

2

Work for Probelm 1

3

2. My eldest daughter is what you might call a picky eater. When my wife makes chocolate chip cookies my daughter will refuse to eat them if they don’t have the right number of chips. Specif- ically she will grab a handful of five cookies, and if 2 or more of the cookies are lacking in chips she will refuse to eat any of them. Assuming that a batch consists of four dozen cookies and the 8 of the cookies will not meet her expectations, what is the probability that she will refuse to eat any of the cookies?

For full credit make sure to clearly identify the following:

(a) Which Distribution this is, or Detailed reasoning for how you counted P (x) = successes

total

(b) The formula you used with variables

(c) the numeric values for each of those variables

(d) the solution

4

3. Poker is a fun game which was more than a little popular when I was back in college. To that end as a math major I played around with figuring out the different odds of winning with certain hands, wrote a program to simulate games of ’Texas Hold’em’ and ’five card draw’. I even won a few tournaments back in the day using my math skills.

What I want you to do is calculate the probability of being dealt a full house when being dealt five cards. (A full house is when you are dealt both a matching pair of cards and a set of three cards that match, think 3 kings and 2 Aces)

Again for full credit try your best to fully explain why you counted the way that you did. And yes the solution is on the internet and I will be taking your phases and matching them to Wikipedia and Other Sites to make sure that the explanation is yours.

5

4. Lets say that a certain stretch of the coast is currently suffer- ing from a toxic algae bloom and the the crabbers that fish this area have no clue that they might get poisoned when they eat the crabs. Let say that seven crabs out of every five hundred is going to carry enough of the toxin to get you sick when eaten.

(a) If you bought a pot of ten of these crabs to have with friends, what is the likelihood that one of you would get sick?

(b) Would this number change if one of the crabs was not eaten? Either way explain why it would or would not change?

For full credit please reference and use the appropriate distri- bution to support you claim.

6

Work for Problem 4

7

5. In recent years a lot of very popular shows have started to boast higher and higher kill counts. And since a number of these shows have become gone on to be the most popular and successful shows in recent history tracking their ”kill counts” has become a thing. And so with all this information lets do some math! Assuming that that probability of any character being killed during an episode of Game of Thrones is 40% find the following

(a) The probability that exactly on character dies in 3 episodes

(b) The probability that at most 5 characters die in 1 episode

(c) Between 10 and 20 characters die in a season of 12 episodes

Again for full credit identify the distribution defend you reason- ing, show both the formula with variables and with the actual numbers you used.

8

6. With the creation of the internet, specifically Social Media and apps like Yelp, IMDB, and Rotten Tomatoes etc, it really has become a world full of critics. More to the point a lot of these ’critics’ have discovered that they get more click troughs, peo- ple reading and interacting with their site, by writing horrible, negative reviews for whether the thing that they are reviewing was good or not. Find the following probabilities assuming that the likely hood of getting a negative review is 80%.

(a) Finding exactly 7 bad reviews out of 10 total

(b) Finding more than 3 bad reviews out of 10

(c) Finding less than 8 good reviews out of 10

(d) Finding between 4 and 7 bad reviews out of 10

9