Probability and Expected Values

A Family Planning Strategy:
By starting this example with the sentence “have children until you have a girl” the author gives like an introduction of what he is about to explain. In this example Nob Heckard gives an introduction of what the expected value is. He explains expected value as “the theoretical mean for a large sample or many repeats of a process”. Therefore, this is how we understand that expected value is the probability of things happening in the long term. In the example Bob shows that there is a 50% chance for the baby to be a girl, and the other 50% to be a boy. After some calculations he found that Expected value could be found by adding the multiplication of the “value and probability” of all the things we are trying to combine. By doing this you can find that the sex mix of boys-girls stays equal.

Swedish Parking Example:
Rather than having meters the policemen look at the air valve’s position on two of the car wheels. If the valves to not move after the hours (the maximum parking time) then the car is ticketed. However, some car owners would argue that they moved the car, parked in the same place, and the valves happened to end up in the same position as before. The multiplication rule must be used to find the probability of this, since the problem is conditional. If the person takes two of the car wheels and compares the valves position to a clock (having 12 likely positions) then one could assume p(1/12)x p(1/12) = 1/144. The one stands for the likelihood of the valve being in the one position it was in before and the 12 stands for the 12 different positions possible. A person’s probability to park their car in the same way is 1/144.

A Roulette Wheel:
First, one must realize that there are 38 numbers total. Take for example that the probability of winning $35 is 1/38. The probability of losing $1 would then be 37/38. In order to calculate the expected value, however, one must incorporate the total value to come to the accurate value. The chance of winning $35 times the actual probability subtracted from the chance of losing $1 is equal to $0.05. Considering the long term effects, neither side truly gains anything. Thus making roulette an unfair game.

Gas Prices, What Can Our Generation Do?

Over the past couple of years the gas prices in America have been a big problem because they keep rising to unpredictable prices. I remember one way that people in America tried to counter act these rising prices was for everyone in America not to buy gas on one day. In theory making the gas companies lose large sums of money that day, sending the message that the consumers control the prices. This of course fails for two reasons; for one not everyone in America participated, probably not very many at all and two, gas companies know that people still need to buy gas.
My proposal for lowering gas prices would be a little different. After taking discrete math, I realize that the consumer does control the market in some ways. Mathematically as a generation we can over come the rising prices of gas by controlling the market. Instead of not buying gas at all for one day, what we can do is not buy gas from the big corporations like BP, Shell, Exxon, or Mobil and buy from the smaller mom and pop gas stations and companies. This will cause the large corporations to lower their prices to match these smaller companies so that they two can make as much money as they used too. Our generation would successfully be mathematically controlling the market by creating a price war between gas competitors.

According to the Article “What is Market Efficiency?”, what are:

Efficient Market Hypothesis (EMH)

An efficent market hypothesis says that no person can out preform the market, because at the end of the day everything evens out. Although it may seem like some people come out with better outcome, in the end some people buy low on the market but some people buy high, but someone has to be buying and selling whether it be low or high. The fluxuation of the market is unpredicable, but the market will always be ontop when everything is said and done.

Behavioral Finance

Behavioral Finance is when people believe that they have mastered the fluxuations of the stock market and feel that they can predict what is going to happen next, they begin making psychologicaly based theories about the market. People try and look at the market and find characteristic that will help create a long term prediction about the market.

January Effect

During the month of January there is an increase in stock prices due to many shareholders selling stock after the month of December because they feel like after christmas the stock has hit its peak and the fear of tax loss. Now that people are“using tax-sheltered retirement plans” the January effect has become more or less unimportant because there is no longer the fear of tax lose.

"How does a market become efficient?"

The ideas and schemes that investors come up with are what keep the market efficent. When pinvestors feel like they can beat the market they come up with irrational ideas that end up putting more money into the market, making it more efficent.

My Ideal Car

My idea car would be a car that will last a long time, long enough to at least out live its depreciation value. Sometimes I wrestle with the idea of leasing a car or owning a car, but both seem equally as risky. When leasing a car I would not have to pay as much per month as owning a car. Another reason is that I could always bring the car back and trade it in for a newer car of my choice at the end of the lease. The downside to leasing is that if you go over the set number of miles for the leasing time or bring the car back with even a minor damage the leasing company will heavily charge you. The good part about owning a car is, you own it. The downside is that you pay a higher monthly fee and you lose money for the cars depriciation. My ideal car would have to be a Mercedes-Benz because it last a long time, or atleast longer than its deprciation value, it has a great miles per gallon ratio, and it is very easy on the eyes.

Greenback Blues Article

In the article Greenback Blues, by James Surowiecki, he discuses the finanical stregth of the American dollar and its decline. Even euros and Candian money have become equal to the dollar. The author writes that in theory because we spend about 1.8 trillion dollars on imported goods, other countries should be making more money than America. But in American we don’t see the effects of the decline of the dollar because of countries like China. China helps prop the american dollar up by lowering the cost of their goods inorder to compensate for the decline of the american dollar. China lowers their prices because America is their biggest consumer of their chinese goods, and is their prices were to high they wouldn’t have as much of a fluid economy. As a result, China is actually loosing money or atleast not making as much money as they possibly could by lowering their prices to help out the American dollar.

Time and It’s Zones

In today’s world we live in a mathematically based society. Everyday people use mathematically based schedules that guide them through their day. Some people use math as at work, around the house, or even at the playground. Techniqually everyone uses math, whether they are good at it or not; some people actually use math and do not even know that they are using an ancient method used by everyone on the globe. Time is a universal form of mathematics. It is universal because no matter what country a person is from, what language they speak, or what level of math they know, clocks are all read the same exact way.
Some people may ask, “Well how come in different places, there are different times, and time zones?”. A time zone is a region of the Earth that has adopted the same standard time, usually referred to as the local time. Most adjacent time zones are exactly one hour apart. Standard time zones can be defined by geometrically subdividing the Earth's surface into 24 sections, and each section is 15 degrees of longitude apart. The local time in neighbouring zones would differ by one hour.
A common misconception is that, if a person gets on a plane and travels to a country far away and misses his or her normal “standard time” hours in flight, that they have some how been nonexistant for several hours. Another common misconception is that for instance if a person travels to from New York to Las Angeles, which has a 3 hour time difference that they have miraculously traveled back in time. Neither of these theories are true. When traveling a person is in a plane which is traveling faster than the earths roation, thus catching up or passing the sun, which changes the time of day in whichever part of the world that perticular person has traveled to.

Green Energy Leaders

The information gathered from the snapshot and the information gathered from the census data did agree with each other for the states that were used in both sets of data, California and Oregon. However, the snap shop failed to include Washington which used almost double the amount of renewable energy as the other two states. Washington may have been left out because it did not fit the other percentages of data and threw off the percentages for the other states. Other states may not have been included for similar reasons like too little use of renewable energy.

Old Math Versus New Math

Old math versus new math is a phenomenon that is sweeping the world! Old math, or sometimes referred to as traditional math is math that was purely subjective which means that it is all formulated from straight facts. By facts I mean the math problems are done using things like equations that if the right numbers are plugged in the right places will give you the correct answer every time. For example y = mx+b, if the correct numbers are inserted for the variables will always give you a straight line of some sort. This is subjective because it is a known fact that it will always give you the right answer if done correctly. New math is taking the same ideas and principles of old or traditional math and using an objective view instead of subjective. When looking at something objectively a person can add some opinion to their statement or in math, the way they figure out the answer to their problem. For instance a person adding 2+2 could use the same traditional math way and use paper and pencil and write out the answer or they could use Popsicle sticks or pennies.
Some people say that new math is better than old or traditional math, but would agree that traditional math is a better way of learning. Some people have different learning strategies or learning disabilities and may find it difficult to learn traditional math because it is based entirely on facts. Those same people probably like new math better because it lets them throw a little of their own opinion in the way they learn and it also lets them use things that they can identify with better. I believe that new math is a great idea and should be used; however, it should be used for and by younger audiences. Using new math in an office that needs exact numbers to estimate things or plan ahead is not one of the places that new math should be found. In a situation like that traditional math should be used in order to find a more accurate answer. Although when using new math a person may get the same answer when using traditional math the room for error is much greater. A great example of a place for new math would be for lower level math in elementary and middle school where kids have the room for error and will not get fired from school from making a mistake.
In the First link provided, the article is written about the different aspects of the old math versus the new math and its looks at the two types of math with a more subjective lens. The article looks at how the change between the two types of math effect grades and other numerical values that determine ones future. In the second article, it looks at the topic of old math versus new math though an objective view. The author clearly states his opinion that new math is better for the youth of this day and age because they are more hands on but the change between old and new math can not happen to quickly or else there will be confusion and mayhem.

Links:
http://www.gothamgazette.com/article/education/20050929/6/1603
http://www.math.washington.edu/~warfield/news/news139.html
http://luceb.com/mathwiki/index.php?title=Old_Math_versus_New_Math

Social Questions

What are social questions?

Social questions are questions that usually ask the probability of something or refer to the relationship between two or more things that effect a community of people. Math can often answer any question because it is used in pretty much every situation. Social questions are often asked to find answers that are often looked at as statistics or facts. Three examples of what a social question would look like are:

1. How much longer will the sun last before it burns out?
2. What is the probability of seeing the same person twice in New York City?
3. What is the probability of getting married at thirty?