Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Risk Management > Probability Models > Flashcards

Probability Models Flashcards

1
Q

In Risk Analysis we use _____ to measure Uncertainty

A

In Risk Analysis we use Probability to measure Uncertainty

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is Classical Probability?

A

Based on the geometry of the problem

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is Frequency Based Probability?

A

Estimated through relative frequency of occurence

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is Subjective Probability?

A

Measures an individuals degree of personal belief

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

A set of events is ____ if they describe every possible outcome.

A

A set of events is exhaustive if they describe every possible outcome.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

A set of results can be referred to as a ______ (an event is a subset of a ______ ).

A

A set of results can be referred to as a sample space (an event is a subset of a sample space).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

____ Diagrams illustrate the relationship between subsets and sample spaces.

A

Venn Diagrams illustrate the relationship between subsets and sample spaces.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Give an example of

1) A mutually exclusive event.
2) Not mutually exclusive event.

A

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!)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is statistical dependence?

A

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is Conditional Probability?

A

When we eliminate some potential events from the sample space entirely.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the Cumulative Distribution Function (CDF)?

A

It refers to the probability that the value of a random variable falls within a specified range.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q
  • A Random Variable is a ____-valued function on a probability space
  • Lifetime Variables are ____ variables which take non negative values.
A
  • A Random Variable is a real-valued function on a probability space
  • Lifetime Variables are random variables which take non negative values.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

The distribution of a Lifetime Random Variable can be given by the _____ Function (sometimes called the _____ Function)

A

The distribution of a Lifetime Random Variable can be given by the Reliability Function (sometimes called the Survivor Function)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q
  • A variable is discrete if it only takes ______.

* A continuous variable is one for which ______.

A
  • A variable is discrete if it only takes values in a discrete set.
  • A continuous variable is one for which the random variable doesn’t take any particular value with a positive probability.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Bernoulli Variable is either _____ and is used to represent the _____ or _____ of an event.

A

Bernoulli Variable is either 1 or 0 and is used to represent the occurrence or non-occurrence of an event.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Binomial Variables take an integer value between ___ and ___ .

They are important in risk analysis because they act as a _______.

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).

17
Q

Poisson Variables can take _____ values.

It represents a limiting Binomial case, whereby ___ is small and ___ is large.

A

Poisson Variables can take any non-negative integer values.

It represents a limiting Binomial case, whereby p is small and n is large.

18
Q

The most important classes of continuous variables are…?

6 items

A
  • Uniform
  • Exponential
  • Normal
  • Log Normal
  • Gamma
  • Beta
19
Q

True / False?
Uniform is the simplest type of continuous distribution.

It is used in failure modelling and to represent uncertainty.

A

True!
Uniform is the simplest type of continuous distribution.

It is used in failure modelling and to represent uncertainty.

20
Q

True / False?

Exponential usually represents distance between events which occur.

A

False!
Exponential usually represents the TIME between events which occur.

For example, the time between different failure events.

21
Q

True / False?

Normally Distributed has 2 parameters, Location and Scale.

A

True!
It has two parameters, 𝐴 (πΏπ‘œπ‘π‘Žπ‘‘π‘–π‘œπ‘› π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) and 𝐡(π‘†π‘π‘Žπ‘™π‘’ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ).

It is used to represent lifetime variables and many different forms of modelling.

22
Q

True / False?

Log Normally Distributed uses parameters which are different to the Normally Distributed models.

A

False!
It uses 𝐴 (πΏπ‘œπ‘π‘Žπ‘‘π‘–π‘œπ‘› π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) and 𝐡(π‘†π‘π‘Žπ‘™π‘’ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) - which is the same as normal distribution models.

It represents the uncertainty in a failure rate parameter, or sometimes lifetime distribution.

23
Q

True / False?

Gamma uses two parameters, 𝛼 (π‘†π‘π‘Žπ‘™π‘’ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) and 𝛽 (πΏπ‘œπ‘π‘Žπ‘‘π‘–π‘œπ‘› π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ)

A

True!

Gamma uses 𝛼 (π‘†π‘π‘Žπ‘™π‘’ π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) and 𝛽 (πΏπ‘œπ‘π‘Žπ‘‘π‘–π‘œπ‘› π‘ƒπ‘Žπ‘Ÿπ‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ) to represent the uncertainty in a failure rate parameter.

24
Q

True / False?

Beta uses two parameters, 𝑛 and π‘š which are both Shape parameters.

A

True!

Uses the two parameters, 𝑛 and π‘š (both Shape parameters), and represents the uncertainty we have in a probability value.

25
Q
  • Uniform
  • Exponential
  • Normal
  • Log Normal
  • Gamma
  • Beta

Are the most common types of distributions used for ______.

A

These are the most common types of distributions used for Failure Time Modelling.

26
Q

______, is the rate of change of failure against time. A ______ is commonly used to capture different ______characteristics.

A

Degradation, is the rate of change of failure against time. A bathtub curve is commonly used to capture different degradation characteristics.

27
Q

The ______ function provides us with the chance that the item is functioning beyond a specified time.

A

The Reliability function provides us with the chance that the item is functioning beyond a specified time.

28
Q

The ______ functrion gives us the chance that an item fails before the specified time.

A

The Cumulative Distribution Function (CDF) gives us the chance that an item fails before the specified time.

29
Q

The ______ rate provides information about the rate at which failures occur.

A

The Hazzard rate provides information about the rate at which failures occur.

30
Q

The ______ calculates the chance of failures within specified intervals.

A

The Probability Density Function (PDF) calculates the chance of failures within specified intervals.

31
Q

The ______ with rate parameter πœ† has a constant failure rate.

A

The Exponential Distribution with rate parameter πœ† has a constant failure rate.

32
Q

The Poisson Process describes the occurrence of highly unpredictable events using:
(2 things)

A
  • Superposition

* Thinning

Risk Management (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions