Definitions Flashcards
Random
Result is not predictable or contains uncertainty
Probabilistic
Cannot predict which possible outcome will occur but overall pattern over many measurements is determined by a probability distribution
Chaotic system
Modelled by deterministic equations but still show long-term effectively unpredictable behaviour based on extreme sensitivity to initial conditions
Deterministic
An event that occurs with certainty
Relative frequency
Number of occurrences of the outcome, divided by the total number of experiments
A-posteriori probability
When relative frequency approaches a steady value after a large number of experiments. Determined after observing results.
Trial
A given single experiment or measurement
Outcome
Result of a trial
Sample space
Set of all possible outcomes
Discrete
When the sample space contains a finite or countably infinite set of outcomes
A priori probability
Total number of possible successful outcomes that could occur over total number of outcomes that could occur. Determined before viewing any results.
Union
x OR Y occur
Intersection
x AND y occur
Complement x
Not-x occurs
Mutually exclusive
When two events cannot occur together in a single trial
Disjoint
When two events have no overlap
Independent
When the occurrence of two events have no effect on each other
Permutation
A particular ordered selection
Combination
An unordered selection
Random variable
Consists of a sample space of possible numerical values together with a probability of those values
Variance
Mean of the squares minus the square of the mean
Poisson requirements
-The events occur randomly
-Events occur independently
-The events happen singly (one at a time)
-The events happen at a constant rate in space or time
-The Poisson parameter is the average rate at which these events occur in a given space or time
Binomial requirments
-A fixed number of trials
-Each trial is “success” or “failure”
-All trials are independent
-The probability of success p is constant
-The variable, x, is the total number of successes
Central limit theorem
If you perform a large number of trials of a random process, then the probability distribution for the average of the outcomes is approximately a Gaussian (normal) distribution. The greater the number of trials, the better the Gaussian approximation
