# Statistics

We are not concerned with the matter that is uncertain.

Thus we do not study the mechanism of rain; only whether it will rain."

--Dennis Lindley, "The Philosophy of Statistics", The Statistician (2000).

## What is Statistics?

This is the science of the collection, organization, and interpretation of data;
this includes designing the methods for the collection of such data. The word
*statistics*, when referring to the scientific discipline, is singular,
as in "*Statistics is an art.*" Not to be confused with the word *statistic*,
referring to a specific quantity calculated from a set of data and whose plural is
*statistics*.

## What is Statistical Analysis?

Statistical analysis is using the science of Statistics and numerical data for
the purpose of, through analysis and interpretations of mathematical formulas and
observation, making predictions of future events. More formerly, * "manipulation
of numerical or categorical data to predict phenomena..."
*

Some scholars pinpoint the origin of statistics to 1663. Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general.

Because of its empirical roots and its focus on applications, statistics is usually considered to be a distinct mathematical science rather than a branch of mathematics. With its additional tools for prediction and forecasting, using data and statistical models, statistics is applicable to a wide variety of academic disciplines (i.e. natural and social sciences, government, and business).

In applying statistics to a scientific, industrial, or societal problem, it is necessary
to begin with a population or process to be studied. Populations can be diverse topics such
as "*all persons living in a country*" or "*every atom composing a crystal*".
The data collected about this kind of "*population*" constitutes what is called a
time series.

For practical reasons, a chosen subset of the population called a sample is studied - as opposed to compiling data about the entire group. Once a sample that is representative of the population is determined, data are collected for the sample members in an observational or experimental setting. These data can then be subjected to statistical analysis, serving two related purposes: description (summarizes the population data by describing what was observed in the sample) and inference (uses patterns in the sample data to draw inferences about the population represented, accounting for randomness).

Statistics can be effectively applied, making use of numbers or numerical data, to draw conclusions and formulate predictions based on probability; to determine the most probable outcome of an event.

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# Laws of Probability

## What is Probability?

Probability is an expression of knowledge concerning the past, or future, occurrence of an event. Basically, using known terms, such as mathematical terms, to convey the knowledge or believe that an event has occurred or is about to occur.

The scientific study of probability is a modern development, specifically; interest in the mathematics of probability was driven by the raising interest in the games of chance. This may explain as to why probability theory, in the mathematics, is primarily concerned with analysis of random phenomena.

In mathematical terms, a probability of One (1) is used to express how "*certain*" an
event is to occur. Likewise, a probability number is used to express that an event has an
impossible certainty to occur; here the number Zero (0) is used. However, it is not as simple as
it looks in the previous statements. A probability Zero (0) event are not always impossible to
occur, nor probability One (1) events are always "*certain*" to occur; there is such a
thing as "*almost certain*" which is often used when calculating the certainty of
any event occurring.

It would be logical to assume that if all the conditions affecting an event were known, including all outside physical forces, we could predict with certainty the outcome of most any event. But, such assumption would be erroneous, because there is random phenomenon.

Random Phenomenon is concept discovered in the 20th century by physics and governed by the laws of quantum mechanics. This leading to the conclusion that probability theory is absolutely required to describe nature, because no event can be predicted with absolute certainty. All that can be done, this far, is come as close as possible to predicting how likely is an event to occur, and expressing such possibility in mathematical terms.

A formal attempt to formalize probability is what gave way to the formulation of the
laws of probability, namely the "*additive*", "*multiplication*" and "*
conditional*" laws.

## Laws of Probability

The Additive Law has two rules; "*
general rule of addition*" and "*special rule of addition*". The general rule
of addition states that when two or more events will happen at the same time, and the
events "*are not mutually exclusive*", then the formula P(X or Y) = P(X) + P(Y) -
P(X and Y) is applied. Therefore, to calculate the probability that a card, chosen at
random from a deck of cards, will either be a king or a queen is P(King or Queen) =
P(X or Y) = 4/52 + 13/52 - 1/52 = 30.77%

The special rule of addition states that when two or more events will happen at
the same time, and the events "*are mutually exclusive*", then the formula
P(X or Y) = P(X) + P(Y) is applied. For this example assume we are packaging 3 lbs of
produce in plastic bags. Most of the bags contain the correct weight, but some of the
bags might be slightly underweight or overweight. A check of some packages in the past
indicates:

Weight.................Event............No. of Packages.........Probability

Underweight.............X...................100.....................0.025

Correct weight...........Y.................3600.....................0.900

Overweight................Z...................300.....................0.075

Total.............................................4000.....................1.00

Then, to calculate the probability of selecting a package, at random, and having the a bag that is under weight or over weight ( remember that the events are mutually exclusive, bag cannot be underweight and overweight at the same time): P(X or Z) = P(0.025 + 0.075) = 0.1

The Multiplication Law, also, has
two rules. The "*general rule of multiplication*" stating that if two or more
events will happen at the same time, and the events "*are dependent*", then to
find the joint probability the formula P(X and Y) = P(X) x P(Y|X) is applied.
Then, if we are interested in selecting one card at random from a deck of cards and
calculating the probability that the card is an Ace and a diamond. P(Ace and diamond)
= (4/52) . (1/4) = 1/52 which is = P(diamond and Ace) = (13/52).(1/13) = 1/52.

The special rule of multiplication states that when two or more events will happen
at the same time, and the events "*are independent*", then P(X and Y) = P(X) x P(Y)
is used to find the joint probability. Therefore, if two coins are tossed, to calculate
the probability of getting a tail on the first coin and a tail on the second coin we say
that P(T and T) = (1/2) x (1/2) = 1/4 = 25%. Let us point-out that in games of chance,
such as roulette and craps, consist of independent events. The next occurrence on the
die or wheel should have nothing to do with what has already happened.

The Conditional Law is based in the knowledge of one of the variables in the event. Then, the conditional probability of an event "X" occurring, given that another event "Y" has occurred (in the case of two dependent events) is calculated P(X|Y) = P(X and Y) / P(Y) = {P(X) x P(Y|X)} / P(Y). However, if the two events are independent: P(X|Y) = P(X) and P(Y|X) = P(Y). For this example, when selecting a card at random, from a standard deck of cards, the probability that the card is an Ace given that it is a diamond is calculated P(Ace given diamond) = P (X|Y) = {P(X) .P(Y|X)} / P(Y); then P(Y) = 13/52, and P(Ace given diamond) = 1/52, thus P(Ace given diamond) = P(X|Y) = (1/52) / (13/52) = 1/13

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# Luck

## What is luck or chance?

Luck (*also refer as providence, chance, fate, or good fortune*) is the possibility,
due to favorable circumstances, an unpredictable phenomenon will cause an event to
have one result rather than another.

Although *"luck"* and *"chance"* are synonyms, in present times,
they were distinct concepts in ancient Greek philosophy. Luck was believed to
operate in the mind and chance was believed to operate in the realm of nature.

Currently, there are many that believe in the predictability of luck.
Such believe is based on the existence of *"luck factors"* or key areas
of a person's life that have direct influence on their future success; consequently,
a person can take control of chance and force favorable outcomes, bring good luck,
into their lives.

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# Psychic Abilities

## What is a Psychic?

Using a strict definition, a psychic
[from the Greek *psychikos*-"of the soul, mental"] is any person able
to use other-than-ordinary sensory perception to render them sensible to things
beyond the natural range of perception. Generally, they have a condition that makes
them susceptible to paranormal, supernatural influences, and non-physical influences.

Psychic gifts or abilities are of diverse nature: Psychometry-this is the ability to perceive things through the use of an object belonging to a person; Clairvoyance-this is the ability of seeing or perceiving things others can't, to include communicating with the dead; and, Precognition-this is the ability to predict future events.