Simulations

Law of large numbers

A statistical principle stating that as the number of trials in an experiment increases, the sample mean will converge to the expected value, making it a fundamental concept in probability and statistics.

Sample mean

is the average of a set of values, calculated by dividing the sum of the values by the number of observations. It becomes a more accurate estimate of the population mean as the sample size increases.

0 probability

refers to an event that is impossible and has no chance of occurring in a given statistical model. In probability theory, it is denoted as 0.

1 probability

refers to an event that is certain to occur within a statistical model, signifying a complete guarantee of occurrence. In probability theory, it is denoted as 1.

Myth of Short run regularity

Incorrectly assumes if randomness has a predictable pattern in the long run, predictions can be made with a smaller dataset.

Simulation

a method used to model and analyze complex systems or processes by imitating their behavior over time. Imitation of a chance behavior based on a model that accuratly reflects the situation.

Myth of Law of averages

Incorrectly assumes past independent events will influence future independent events, leading individuals to believe that outcomes will 'even out' over time.

Probability models

mathematical frameworks used to represent random phenomena, allowing for the estimation of probabilities of various outcomes.

Sample space

the set of all possible outcomes in a probability experiment. (S)

Event

a subset of the sample space representing one or more outcomes.

P(A)

represents the probability of event A occurring.

Complement

the set of outcomes in the sample space that are not included in event A.

Disjoint/Mutually exclusive event

events that cannot occur simultaneously in a probability space.

General additon rule of events

states that the probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.

General additoon rule of events formula

P(A or B) = P(A) + P(B) - P(A&B)