What Is the Expected Value in Probability

Youre at a carnival and you see a game. For $2 you roll a standard six-sided die. If the number showing is a six you win $10, otherwise, you win nothing. If youre trying to make money, is it in your interest to play the game? To answer a question like this we need the concept of expected value. The expected value can really be thought of as the mean of a random variable. This means that if you ran a probability experiment over and over, keeping track of the results, the expected value is the average of all the values obtained. The expected value is what you should anticipate happening in the long run of many trials of a game of chance. How to Calculate the Expected Value The carnival game mentioned above is an example of a discrete random variable. The variable is not continuous and each outcome comes to us in a number that can be separated out from the others. To find the expected value of a game that has outcomes x1, x2, . . ., xn with probabilities p1, p2, . . . , pn, calculate: x1p1 x2p2 . . . xnpn. For the game above, you have a 5/6 probability of winning nothing. The value of this outcome is -2 since you spent $2 to play the game. A six has a 1/6 probability of showing up, and this value has ​an  outcome of 8. Why 8 and not 10? Again we need to account for the $2 we paid to play, and 10 - 2 8. Now plug these values and probabilities into the expected value formula and end up with: -2 (5/6) 8 (1/6) -1/3. This means that over the long run, you should expect to lose on average about 33 cents each time you play this game. Yes, you will win sometimes. But you will lose more often. The Carnival Game Revisited Now suppose that the carnival game has been modified slightly. For the same entry fee of $2, if the number showing is a six then you win $12, otherwise, you win nothing. The expected value of this game is -2 (5/6) 10 (1/6) 0. In the long run, you wont lose any money, but you wont win any. Dont expect to see a game with these numbers at your local carnival. If in the long run, you wont lose any money, then the carnival wont make any. Expected Value at the Casino Now turn to the casino. In the same way as before we can calculate the expected value of games of chance such as roulette. In the U.S. a roulette wheel has 38 numbered slots from 1 to 36, 0 and 00. Half of the 1-36 are red, half are black. Both 0 and 00 are green. A ball randomly lands in one of the slots, and bets are placed on where the ball will land. One of the simplest bets is to wager on red. Here if you bet $1 and the ball lands on a red number in the wheel, then you will win $2. If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on a bet such as this? Since there are 18 red spaces there is an 18/38 probability of winning, with a net gain of $1. There is a 20/38 probability of losing your initial bet of $1. The expected value of this bet in roulette is 1 (18/38) (-1) (20/38) -2/38, which is about 5.3 cents. Here the house has a slight edge (as with all casino games). Expected Value and the Lottery As another example, consider a lottery. Although millions can be won for the price of a $1 ticket, the expected value of a lottery game shows how unfairly it is constructed. Suppose for $1 you choose six numbers from 1 to 48. The probability of choosing all six numbers correctly is 1/12,271,512. If you win $1 million for getting all six correct, what is the expected value of this lottery? The possible values are -$1 for losing and $999,999 for winning (again we have to account for the cost to play and subtract this from the winnings). This gives us an expected value of: (-1)(12,271,511/12,271,512) (999,999)(1/12,271,512) -.918 So if you were to play the lottery over and over, in the long run, you lose about 92 cents — almost all of your ticket price — each time you play. Continuous Random Variables All of the above examples look at a discrete random variable.  However, it is possible to define the expected value for a continuous random variable as well.  All that we must do in this case is to replace the summation in our formula with an integral. Over the Long Run It is important to remember that the expected value is the average after many trials of a random process. In the short term, the average of a random variable can vary significantly from the expected value.

Macroeconomic Objectives Of The Malaysian Economy

Four macroeconomic objectives In this section I will be discussing how well does Malaysia manage to achieve the four macroeconomic objectives which are; high and stable economic growth, low unemployment, low inflation and avoidance of large balance of trade deficit. One of the ways that Malaysia’s economy plan to reach the goals of high and stable economic growth is by implementing a fiscal consolidation â€Å"The Malaysian government has embarked on fiscal consolidation† (Ratings and Investment Information, Inc, 2014) through using fiscal policy the Malaysian government are able to help drive the growth of the economy, as well as a statement from the Prime Minister Datuk Seri Najib where he said â€Å"The increase in petrol price is a process to strengthen the economy in the short and medium term† (Bernama, 2013) by increasing the price of fuel it will enable to generate more money into the economy thus resulting in the surge of growth in the short and medium term, however this is not a long term plan. One the main feature of the Malaysian economy has been to have a low and stable rate of inflation in the past couple of decades. The current inflation rate in October 2014 was at â€Å"2.80%† (Trading Economics , 2014) this shows that inflation is currently at a steady pace. Figure 1.2 (Trading Economics, 2014) Figure 1.2 shows how the trend in inflation has been for the past 25 years showing the inflation rates have been increasing and decreasing as a steady rate and on average hasShow MoreRelatedImportance of the Macroeconomics Objectives Towards the Malaysia Economic Performance.1564 Words   |  7 Pages| 2.0 | Macroeconomic Objectives | 4 | 3.0 * 3.1 * 3.2 | Economic GrowthThe ImportanceExample | 556 | 4.0 * 4.1 * 4.2 | UnemploymentThe ImportanceExample | 778 | 5.0 * 5.1 * 5.2 | InflationThe ImportanceExample | 9910 | 6.0 | Conclusion | 11 | 7.0 | References | 12 | 8.0 | Appendix | 13 | 1.0 Introduction This assignment is to discuss the importance of the Macroeconomics Objectives towards the Malaysia economic performance. 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The Purpose of a Liberal Arts Education Free Essays

A liberal arts education can open many doors for you. However, it may not be for everyone. A four year liberal arts degree is meant to make you a well-rounded person, but many people don’t feel the need to take classes that don’t directly apply to their career. We will write a custom essay sample on The Purpose of a Liberal Arts Education or any similar topic only for you Order Now Liberal arts exercises your mid; it makes it stronger. It helps develop an ordered mind and good thinking habits. You may never use the things you learn in a computer programming class, but it will make you a better learner. It also teaches you to think for yourself; your fellow students and teachers will challenge what you know, think and believe. Imagine the doors of creativity that will be opened for you. You may not have known how much you enjoy paining until you took a mandatory general education art class. It can enhance your faith. Maybe you have an interest in taking a theology class so you can be closer to god, at a liberal arts college you can have that opportunity. You can better understand the bible, who wrote it, and why they were inspired to do so. A liberal arts education will not only make you a better learner, it will also make you a better teacher. The more molded your mind becomes, the more easily you can explain things to people. Even if you don’t plan on becoming a professional teacher, this can help you help your children with their homework, help train new employees, or even teach a Sunday School class. It will cultivate your mind; opening doors to art, music, symbolism, or even language, things you may not have even had an interest in before. You will learn to appreciate these things more. A Christian liberal art education may be the right thing for you. It can send you in the right direction if you want to teach in a private Christian school, want to be a missionary, a pastor, or even if you just want to be education with fellow Christians. Some of your classes may cause you to question not only your faith, but why you have it in the first place, which will make you see why you fell in love with God in the first place. But does this mean a liberal arts education is right for everyone? I don’t believe it does. A single mother going back to school may not have time for the required number of classes, most of which, she will never use on the job. A 40 year old works at a factory that is being shut down and he needs to learn a new skill quickly so he can go back to supporting his family. For people like this, a liberal arts education may not be the right road for them to take. A liberal arts education can do many more things for you than what I have mentioned. It’s like a treasure trove; you have the key, all you have to do is open the door and that wealth of knowledge could be yours. How to cite The Purpose of a Liberal Arts Education, Papers

India-Bangladesh Relations free essay sample

The  non  trade  barriers,  as  pointed  out  by   Bangladesh  Commerce  Ministry,  and  cited   by  the  Daily  Star  include:  2   ? Laboratory   tests   in   Bangladesh,   especially   for   food   products,   cosmetics,   and   leather   and   textiles   products. ? Packaging  requirements   ? Inadequate   infrastructure   facilities   such   as   warehousing,   transshipment   yard,  parking  yard  and  Ã‚   ? Connecting   roads   at   land   customs   stations   also   hinder   exports   from   Bangladesh;   the   land   border   trade   is   subject  to  very  serious  administrative   constraints   in   Bangladesh. The   most   important   of   the   Customs   posts   with   comprehensive   Customs   clearance   powers  is  at  Benapole,  which  borders   Petrapole   on   the   Indian   side   and   which   is   on   main   roads   linking   Kolkata  with  Jessore  and  Dhaka. As   per   the   report   by   Bangladesh   Commerce   Ministry,   trade   barriers   include:3   Sajjadur Rahman, â€Å"Analysts urge India to erase trade barriers to Bangladesh†