Law of Numbers - Essay Example

Only on StudentShare

Extract of sample
Law of Numbers

[2]
If a coin is tossed many times, the more times it is tossed, the likelihood of the number of "heads" in the total population will be close to 1/2. This Law of Large Numbers can be further explained with the help of a Randomly Generated Coin Toss online applet (available from http://hspm.sph.sc.edu/COURSES/J716/a01/stat.html).
The coin is unbiased and it has two sides that are equally likely to come up. When the random generator is run, the applet shows the proportion of heads in the total population. In the first 10 tosses the proportion of heads is 0.272 (3 heads and 7 tails). When it is run for a longer time up to 100 tosses the proportion of heads approaches one-half and becomes 0.48 (43 heads and 47 tails). For a 1000 tosses the proportion of heads become 0.499 (502 heads and 498 tails). This figure will fluctuate around 0.5, with the fluctuations slowly getting smaller and almost reaching 0.5. [1]
1) Let's say you flipped the coin once and it landed on heads. You will expect that on alternative tosses you will get a head. In 10 coins are tossed you expect 5 to be heads since the expected percentage of successes is 50%. But in reality only three are heads. The difference between the actual and expected number of successes is 2. The actual percentage of number of heads is 20% meaning a difference between actual and expected percentage of 30%. ...
Download paper

Summary

The law of large numbers (LLN) explains that as the number of trials increase, the random variable becomes stable in the long-run. If a trial of probable situation is repeated again and again, then the more times the trial is repeated, the more likely it is that the frequency of any particular event will be close to the probability of that event…
Author : makenzieruecker

Related Essays

International Human Rights Law
The concept of international protection of individual rights was expressly recognized in the San Francisco Conference (1945). The United Nations Charter also imposed human rights obligations on all member states, pursuant to which the General Assembly approved the Universal Declaration of Human Rights (1948). These international documents show the desire of the international community to recognize individuals as partial subjects of international law. Although the Universal Declaration is not a legally binding document, several states have voluntarily included in their national constitutions...
11 pages (2761 words) Essay
Women in law enforcement
According to (Jon Felperin, 2005) in 1845, the first women to be hired by the New York City Police Department were called "matrons." In 1985, Penny Harrington of the Portland Oregon Police Department became the first female Chief of Police, Today, once the last bastion of male domination in the workplace, police organizational attitudes are finally beginning to change. And yet serious problems still remain.
...
8 pages (2008 words) Essay
NUMBERS DROP FOR MARRIED WITH CHILDREN
To be more precise and clear, a few statistical data can be taken into consideration. Over the last five decades, cohabiting couples in the United States have increased tenfold from 0.44 million to 4.2 million. Divorce rates have increased from 9 to 20 per 1000 married couples for the same period. Births to unmarried women have increased from 11% to 38% from 1970 to 2006. Nationally, more than 1.3 million children are born out of wedlock each year. While cohabitation, divorce and unmarried childbearing have increased, marriage in America has alarmingly declined over the last few decades....
3 pages (753 words) Essay
EU LAW
We will begin with a concise yet comprehensive overview of the European Union and will thoroughly address the evolution of the EU following the collapse of state-led communism in Eastern Europe. The European Union has undergone a variety of changes in the aftermath of the fall of the Soviet Union including expansion to the east through the Maastricht Treaty and proposed institutional change through the Treaty of Lisbon.
...
12 pages (3012 words) Essay
Working With Numbers and Formulas
Use Okun’s law to determine the size of the GDP gap in percentage-point terms. If the potential GDP is $500 billion in that year, how much output is being forgone because of cyclical unemployment?
...
20 pages (5020 words) Speech or Presentation
Law
Significant to the argument, is the relatively low number of offenders charged and convicted under the existing rules. Part of the challenge seems to lie in what critics argue is the vagueness of the law that is rendered even less clear in court, as it is impossible for a supplier to assess the ‘likelihood’ that an internet or software tool may be used in the commission of a crime. Opponents cite that the CMA does not allow for application of the rules to the cases which are often highly technical, and not readily translatable for jury consideration. The results are near null from a...
12 pages (3012 words) Coursework
Quadratic Equations and Prime Numbers
Prime number is defined as the number divisible by 1 or itself. A prime number has only two factorization 1 and the number itself. Mathematicians have been searching for a formula that yields prime numbers and found one such formula as (Bluman, 2005). This paper will use this formula for yielding prime numbers and verify extent to which it can generate prime numbers.
Therefore, it can be seen that the yields prime number for smaller values of x. The formula will not yield prime number when the term will be zero as will be divisible by x. Therefore, putting the term equals to
2 pages (502 words) Speech or Presentation
Got a tricky question? Receive an answer from students like you! Try us!