Probability Models Flashcards
In Risk Analysis we use _____ to measure Uncertainty
In Risk Analysis we use Probability to measure Uncertainty
What is Classical Probability?
Based on the geometry of the problem
What is Frequency Based Probability?
Estimated through relative frequency of occurence
What is Subjective Probability?
Measures an individuals degree of personal belief
A set of events is ____ if they describe every possible outcome.
A set of events is exhaustive if they describe every possible outcome.
A set of results can be referred to as a ______ (an event is a subset of a ______ ).
A set of results can be referred to as a sample space (an event is a subset of a sample space).
____ Diagrams illustrate the relationship between subsets and sample spaces.
Venn Diagrams illustrate the relationship between subsets and sample spaces.
Give an example of
1) A mutually exclusive event.
2) Not mutually exclusive event.
1) A card can be black or red.
2) A card is red or less than 7 (i.e. it is possible to be both!)
What is statistical dependence?
When one probability relies on another, e.g. removing an ace from a deck means changes the odds of drawing another ace from the deck again.
What is Conditional Probability?
When we eliminate some potential events from the sample space entirely.
What is the Cumulative Distribution Function (CDF)?
It refers to the probability that the value of a random variable falls within a specified range.
- A Random Variable is a ____-valued function on a probability space
- Lifetime Variables are ____ variables which take non negative values.
- A Random Variable is a real-valued function on a probability space
- Lifetime Variables are random variables which take non negative values.
The distribution of a Lifetime Random Variable can be given by the _____ Function (sometimes called the _____ Function)
The distribution of a Lifetime Random Variable can be given by the Reliability Function (sometimes called the Survivor Function)
- A variable is discrete if it only takes ______.
* A continuous variable is one for which ______.
- A variable is discrete if it only takes values in a discrete set.
- A continuous variable is one for which the random variable doesnβt take any particular value with a positive probability.
Bernoulli Variable is either _____ and is used to represent the _____ or _____ of an event.
Bernoulli Variable is either 1 or 0 and is used to represent the occurrence or non-occurrence of an event.
Binomial Variables take an integer value between ___ and ___ .
They are important in risk analysis because they act as a _______.
Binomial Variables take an integer value between 0 and n.
They are important in risk analysis because they act as a model of redundant systems.
(For example, a safety system will operate as long as one of the available safety systems work).
Poisson Variables can take _____ values.
It represents a limiting Binomial case, whereby ___ is small and ___ is large.
Poisson Variables can take any non-negative integer values.
It represents a limiting Binomial case, whereby p is small and n is large.
The most important classes of continuous variables are�
6 items
- Uniform
- Exponential
- Normal
- Log Normal
- Gamma
- Beta
True / False?
Uniform is the simplest type of continuous distribution.
It is used in failure modelling and to represent uncertainty.
True!
Uniform is the simplest type of continuous distribution.
It is used in failure modelling and to represent uncertainty.
True / False?
Exponential usually represents distance between events which occur.
False!
Exponential usually represents the TIME between events which occur.
For example, the time between different failure events.
True / False?
Normally Distributed has 2 parameters, Location and Scale.
True!
It has two parameters, π΄ (πΏππππ‘πππ πππππππ‘ππ) and π΅(πππππ πππππππ‘ππ).
It is used to represent lifetime variables and many different forms of modelling.
True / False?
Log Normally Distributed uses parameters which are different to the Normally Distributed models.
False!
It uses π΄ (πΏππππ‘πππ πππππππ‘ππ) and π΅(πππππ πππππππ‘ππ) - which is the same as normal distribution models.
It represents the uncertainty in a failure rate parameter, or sometimes lifetime distribution.
True / False?
Gamma uses two parameters, πΌ (πππππ πππππππ‘ππ) and π½ (πΏππππ‘πππ πππππππ‘ππ)
True!
Gamma uses πΌ (πππππ πππππππ‘ππ) and π½ (πΏππππ‘πππ πππππππ‘ππ) to represent the uncertainty in a failure rate parameter.
True / False?
Beta uses two parameters, π and π which are both Shape parameters.
True!
Uses the two parameters, π and π (both Shape parameters), and represents the uncertainty we have in a probability value.
- Uniform
- Exponential
- Normal
- Log Normal
- Gamma
- Beta
Are the most common types of distributions used for ______.
These are the most common types of distributions used for Failure Time Modelling.
______, is the rate of change of failure against time. A ______ is commonly used to capture different ______characteristics.
Degradation, is the rate of change of failure against time. A bathtub curve is commonly used to capture different degradation characteristics.
The ______ function provides us with the chance that the item is functioning beyond a specified time.
The Reliability function provides us with the chance that the item is functioning beyond a specified time.
The ______ functrion gives us the chance that an item fails before the specified time.
The Cumulative Distribution Function (CDF) gives us the chance that an item fails before the specified time.
The ______ rate provides information about the rate at which failures occur.
The Hazzard rate provides information about the rate at which failures occur.
The ______ calculates the chance of failures within specified intervals.
The Probability Density Function (PDF) calculates the chance of failures within specified intervals.
The ______ with rate parameter π has a constant failure rate.
The Exponential Distribution with rate parameter π has a constant failure rate.
The Poisson Process describes the occurrence of highly unpredictable events using:
(2 things)
- Superposition
* Thinning
