Law of Numbers

College
Essay
Miscellaneous
Pages 2 (502 words)
Download 0
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…

Introduction

[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
Not exactly what you need?

Related papers

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…
Family Law: civil partnership
This is clear from the Matrimonial Causes Act of 1973. Pursuant to Section 23 of the said Act, the Court may make several orders that relate to income, capital and property. It may order the payment of periodical payments by either party to the other, or it may also issue an order for the payment of lump sums. an order that either party to the marriage shall pay to the other such lump sum or sums…
Law Essay
Despite these and countless other opportunities, Bin Laden exhibited a persistent tendency towards religious fanaticism and upon the Soviet invasion of Afghanistan, joined the mujahedeen forces.…
Fibonacci numbers and the golden section
Recall that an integer is prime if it has no proper divisors. Some Fibonacci numbers are prime, for example 514229, but it is still unknown whether there exist infinitely many prime Fibonacci numbers. The problem of finding prime numbers with many digits is crucial for the…
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…
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…