Simpson's Paradox
What is the problem?
In this problem we reviewed death sentence data, from that we were then set to decided, based off the facts if death sentences were racially motivated in 1978. We specifically reviewed Warren McClesky's case. Warren McCleasky was a black man, who was convicted of killing a white police officer, and was sentenced to death in a electric chair in Georgia. McClesky was a robber, he was apart of a gang , that gang shot and killed an off-duty police officer. He was sentenced to death 13 years after the crime was committed. McClesky's lawyer argued in an appeal before the U.S. supreme court that the imposition of death penalties in Georgia were racially biased. The data that was given to us to answer the question ( of the people getting the death penalty, do the percentages suggest a difference between white or black criminals getting the death sentence?) was for the state of Florida between 1976 & 1980.
My Process
The process I went through to solve this problem was I looked at the 3 information tables provided. First I looked at the percentages then the number, and when comparing the two i noticed they were totally off. The total number and the percentages didn't provide an accurate answer. This problem was so different from anything I've ever seen before. This is the first time I've ever been introduced to the Simpsons paradox, and it was really interesting to see how with the Simpsons paradox, because when they combined the information you wouldn't really see a huge change but once you saw it individually you could see the huge difference in the graphs.
In this problem we reviewed death sentence data, from that we were then set to decided, based off the facts if death sentences were racially motivated in 1978. We specifically reviewed Warren McClesky's case. Warren McCleasky was a black man, who was convicted of killing a white police officer, and was sentenced to death in a electric chair in Georgia. McClesky was a robber, he was apart of a gang , that gang shot and killed an off-duty police officer. He was sentenced to death 13 years after the crime was committed. McClesky's lawyer argued in an appeal before the U.S. supreme court that the imposition of death penalties in Georgia were racially biased. The data that was given to us to answer the question ( of the people getting the death penalty, do the percentages suggest a difference between white or black criminals getting the death sentence?) was for the state of Florida between 1976 & 1980.
My Process
The process I went through to solve this problem was I looked at the 3 information tables provided. First I looked at the percentages then the number, and when comparing the two i noticed they were totally off. The total number and the percentages didn't provide an accurate answer. This problem was so different from anything I've ever seen before. This is the first time I've ever been introduced to the Simpsons paradox, and it was really interesting to see how with the Simpsons paradox, because when they combined the information you wouldn't really see a huge change but once you saw it individually you could see the huge difference in the graphs.
Other Students Process:
First they looked for the biggest outlier within the 3 information tables provided. After that they compared the percentages to the numbers and based their answer off of the information given. Solution: So looking at all the data you could notice that if there was a white victim both suspects would get a penalty but if a black suspect were to have a white victim against them they would have a higher death penalty making everything completely unfair. |
PROBLEM ASSESSMENT:
I personally did like the problem, because it was based off of a real life situation. My group worked together by looking at the data provided and comparing everything and looking for the outliers.
Self Evaluation:
I would give myself an A on this assignment, because I really looked for anything and everything. I looked for any patterns or off numbers. What I found was a big difference in the numbers they would compare. I tried really hard on this problem to find any little errors that could throw off the total percentages. I would go back and re-compare the information if I found myself second guessing my answer. Also I would talk to my peers and get their opinions on the problem to better understand the problem.
I personally did like the problem, because it was based off of a real life situation. My group worked together by looking at the data provided and comparing everything and looking for the outliers.
Self Evaluation:
I would give myself an A on this assignment, because I really looked for anything and everything. I looked for any patterns or off numbers. What I found was a big difference in the numbers they would compare. I tried really hard on this problem to find any little errors that could throw off the total percentages. I would go back and re-compare the information if I found myself second guessing my answer. Also I would talk to my peers and get their opinions on the problem to better understand the problem.
Birthday Paradox
What is the problem?
In this problem we were looking at the probability of multiple people having the same birthday The problem was asking us, how many people would we need in a group for the probability that two people will have the same birthday to become 50%.
In this problem we were looking at the probability of multiple people having the same birthday The problem was asking us, how many people would we need in a group for the probability that two people will have the same birthday to become 50%.
My Process:
In the beginning I wasn't sure how to even approach this problem, I was working with Bridgette and we both were very confused so before asking anyone on how solve the problem we decided it might be very helpful to go on Khan Academy and look up the problem and see what advice we could get from there. Once on Khan Academy we found how to at least begin the problem, it gave us a recommendation on how to set it up. From there we were set, but we then realized it would take quite a while to get to 50%. That's when we both decided to share what we found with our table partners and have them share with us what they found, and we were both working in the same direction. The only difference was they were working on and equation. I'm personally not very good with coming up with equations so I decided to step back and listen to learn. That is when I learned how adding factorials to the equation would make everything a lot easier. |
Other Students Process:
As I already talked about above, my table partners went through the same process I went through. I think the only difference was Bridgette and I had the exact same process and Chris and Jesus approached it without going through Khan Academy. They automatically went directly to finding an equation.
As I already talked about above, my table partners went through the same process I went through. I think the only difference was Bridgette and I had the exact same process and Chris and Jesus approached it without going through Khan Academy. They automatically went directly to finding an equation.
The Solution: (To the right is an image of Mr. T's Solution)
Assessment:
The problem was a bit complicated because in the beginning I was very confused on how to even begin the problem. It was a bit frustrating, but I'm glad I asked for help from my table partners. I was glad I had the table partners I did because they were very helpful and showed me how to see the problem a bit clearer. Self Evaluation: I would give an A on this problem, because I did something I haven't done in a long time which is go online and find help for myself. I was able to understand what the problem was asking me and find a way to set up the problem and my by myself and obviously with the help of my table partners find an answer. |
Ferris wheel Problem
Problem Statement:
There is a diver standing on a platform of a ferris wheel.The ferris wheel is moving counter clockwise at a speed of 40 ft/s. The objective of the diver is to dive into a moving cart of water that will pass by the ferris wheel at 15 ft/s. The overall question was “at what time should the the diver jump from the platform?”
There is a diver standing on a platform of a ferris wheel.The ferris wheel is moving counter clockwise at a speed of 40 ft/s. The objective of the diver is to dive into a moving cart of water that will pass by the ferris wheel at 15 ft/s. The overall question was “at what time should the the diver jump from the platform?”
My Process: First we started to try and figure out how far the diver was from ground. We used this equation (65+50sin9t) to figure out how to get to height from the ground to the diver. The 65 was the height from the center to the ground, the 50 was the radius and the 9 was the degrees/second, and lastly for the t you would insert the time. Then with soh cah toa we were able to figure out the platforms height off the ground. Then with the 30-60-90 triangle we figured out how far was off the ground at any position. We then discovered the formula for the diver's horizontal position at any given time. Then we learned that the speed of the moving cart was 15 ft/s on a 240 ft track and the cart contained 8 ft of water.
(To the right are pictures of notes or any work done in class to help better understand this problem.) Other Students Process:
Most students process was the same as to what I wrote above, that is because we sorta worked on this problem together as a whole class. Assessment:
Overall this problem was the longest problem I've ever encountered in my life. There was many moments where I hated this problem and to just over with it, but I did learn a lot from it. I mostly listened to what people had to say about the problem instead of participating on my own, because I'm barley beginning to be comfortable with math to solving this problem on my own was something I wasn't ready for because of how long it was. |
The Solution:
The answer to the problem was, 12.28 seconds. The main equation we used to solve for the answer was -240 + 15t + 15 x √57 +50 sin (9t)/16. Self Evaluation:
I would give myself a B+. The reason for giving myself this grade is because, I tried my hardest to understand this problem and everything we did throughout it. Like I spoke about in the assessment portion I spent a lot of time listening instead of sharing my own thought the reason I did that was, because for a lot of this problem we had no specific directions on what to do. So what I would do then is listen to my peers and see what way they would approach the problem and why. So I still learned a lot from the problem, but I do wish I had attempted to find more of the equations on my own. The good thing is now I know how start finding equations and solving them. |
Fry's Bank
Problem Statement:
This problem was asking us to find how much money Fry would have in his bank account if he only had 93 cents in the beginning but his money had been in the bank for 1000 years at the annual interest rate of 2.25. The process other people went through:
the process other people went through to solve it was exactly the same to the process I went through. The reason I say this is based off the people I worked with and the how the whole class shared their solutions at the end. Solution:
The answer to the problem was 4.28350845x10(9) billion dollars. Assessment:
I think this assignment was very interesting. I had prior knowledge that If you left your money in your bank account untouched with good interest rate eventually you would be making a lot of money. What this problem did teach me is an estimate of how much money you could eventually be getting. Also how to find the exact amount you be getting in x years. Another thing is if would be worth it to ever leave money in my bank account just to make more in the end. The answer to that is hell yeah if I had enough money to leave in my bank account I so would. |
Process:
The process I went through to solve this problem was to use logarithms. We figured out what we would need find out what would be a number that was to high then a number that was too low. We figured out that 1 billion would be two low, and that 1 trillion would be to high. After that the whole class got together and we put it into an equation that looked like this 0.93 (1+0.0225) to the 1000 power. The 0.93 would be the number in which he started with in his bank account. Then the (1+0.0225) is the because that is the annual interest rate, the 1 is added so the number wont get halved when multiplied. Also it is to the 1000 power because Fry had he money in his bank account for 1000 years. Self Evaluation:
I think for this assignment I deserve an A. I believe this because, I tried really hard on this problem, and I ended learning a lot. I was very engaged in this problem, and understood everything I worked on to solve the problem. |