Actuarial / Statistics

Actuaries

An actuary is a professional business person skilled in the application of mathematics to financial problems. They apply specialized knowledge of the mathematics, finance, statistics and risk theory to problems faced by:

  • insurance companies
  • pension plans
  • government regulators
  • social programs
  • individuals

Traditionally, actuaries have specialized in:

  • life insurance
  • annuities
  • property and casualty insurance
  • pension plans
  • other employee benefit plans
  • evidence in the courts about loss of future earnings

An actuary has a practical business sense, the creativity to apply training and experience to new problems and provide innovative solutions, and the communication skills required to convince both colleagues and clients. Actuaries help people plan better for the future by controlling or reducing financial risks associated with:

  • sickness
  • disability
  • dying too soon
  • living too long
  • unemployment
  • property loss and damage
  • investment policy

Some actuaries spend part of their time ensuring that companies and pension plans comply with the consumer protection and tax legislation which govern their operations. In legislation, an actuary is defined as a Fellow of the Canadian Institute of Actuaries. Actuaries, as a profession, have rules of professional conduct and standards of practice.

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Probability & Chance

Chance is a part of our everyday lives. Everyday we make judgments based on probability:

  • There is a 90% chance the Bulls will win the game tomorrow.
  • There is a sixty percent chance of thunderstorm this afternoon.
  • We have a 50-50 chance of winning the game.
  • There is a 20% chance of rain today.

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Although we assign certain probabilities to certain events, others might assign different probabilities to those same events due to their difference of opinion. For example, not everyone agrees with the high chance of the Bulls winning the game. They might say that there is a 20% chance the Bulls will win the game tomorrow. It all depends on what the person believes. Chance may result from human design such as casino games and the lottery, or it may result from nature such as determining a person’s sex and other human characteristics. Probability is defined as the branch of mathematics that describes the pattern of chance outcomes.

The History of Probability
Probability originated from the study of games of chance. Tossing a dice or spinning a roulette wheel are examples of deliberate randomization that are similar to random sampling. Games of chance were not studied by mathematicians until the sixteenth and seventeenth centuries. Probability theory as a branch of mathematics arose in the seventeenth century when French gamblers asked Blaise Pascal and Pierre de Fermat (both well known pioneers in mathematics) for help in their gambling. In the eighteenth and nineteenth centuries, careful measurements in astronomy and surveying led to further advances in probability. In the twentieth century probability is used to control the flow of traffic through a highway system, a telephone interchange, or a computer processor; find the genetic makeup of individuals or populations; figure out the energy states of subatomic particles; Estimate the spread of rumors; and predict the rate of return in risky investments.

Predictable Occurrences
The time an object takes to hit the ground from a certain height can easily be predicted using simple physics. The position of asteroids in three years from now can also be predicted using advanced technology.

Unpredictable Occurrences
Not everything in life, however, can be predicted using science and technology. For example, a toss of a coin may result in either a head or a tail. Also, the sex of a new-born baby may turn out to be male or female. In these cases, the individual outcomes are uncertain. With experience and enough repetition, however, a regular pattern of outcomes can be seen (by which certain predictions can be made). For example, the result of the next 100 tosses of a coin can be assumed to be 50 heads and 50 tails. Since there are only two possible outcomes, the chances of getting a head or a tail are equal. This describes the basis of the Random Phenomenon:

Random Phenomenon
An event or phenomenon is called random if individual outcomes are uncertain but there is, however, a regular distribution of relative frequencies in a large number of repetitions. For example, after tossing a coin a significant number of times, it can be seen that about half the time, the coin lands on the head side and about half the time it lands on the tail side.

Probability Theory
Probability Theory is the mathematical study of randomness. This theory deals with the possible outcomes of an event. It must be possible to list every outcome that can occur, and we must be able to state the expected relative frequencies of these outcomes. It is the method of assigning relative frequencies to each of the possible outcomes.

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