Definitions Flashcards

(31 cards)

1
Q

Define Risk Analysis

A

Provides a framework and computational tools for assessing the safety of systems and follow up decision making

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2
Q

Define Risk Measure

A

Product of probability of occurrence and its consequences:

R = P(E)*Ce

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3
Q

What are the three axioms of probability?

A
  1. For every event, E, P(E)≥0
  2. Probability of all events, S, P(S)=1
  3. For mutually exclusive events: P(AuB)=P(A)+P(B)
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4
Q

Define a Random Experiment/Trial

A

Process that may provide different outcomes when observed repeatedly

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5
Q

Define Outcome

A

Each particular possible result off a trial

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6
Q

Define sample space and empty space

A

S or Ω, set of all possible outcomes of the trial

∅, set of no events

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7
Q

Define Event

A

Set of outcomes

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8
Q

Define De Morgan rule

A

Symmetry between the union and inter-section of events through the complementary operator

The complementary of an intersection is the union of complementaries
A ∩ B (full line) = A ∪ B (line over each letter)

The complementary of a union is the intersection of the complementaries:
A ∪ B (full line) = A ∩ B (line over each letter)

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9
Q

Define probability measure and triplet

A

Map P: F->R which satisfies the three probability axioms

Triplet (Ω,F,P) is called probability space

(1) P(A) = 1 − P(A).
(2) P(∅) = 0.
(3) If A ⊂ B, then P(A) ≤ P(B).
(4) For the union of two events, P(A ∪
B) = P(A) + P(B) − P(A ∩ B).

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10
Q

Define Conditional probability

A

Event A occurs given B has occurred

P(A|B) = P(A ∩ B)/P(B) , provided P(B) doesn’t equal 0

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11
Q

Define independence

A

One event does not influence the other

P(A|B) = P(A)

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12
Q

Define Bayes Theorem

A

P(B|A) = (P(A|B)P(B))/P(A)

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13
Q

Define a random variable

A

Mathematical tool for describing an event, maps the the possible outcomes of an event to a number line

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14
Q

Define a discrete random variable

A

Random variable that is finite or countably infinite

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15
Q

Define a continuous random variable

A

Random variable that is an interval of R or a union of intervals

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16
Q

Define a probability distribution

A

Probability X takes a particular value

pk = pX (xk) = P(X = xk) = P({w ∈ Ω|x(w) = xk}), k = 1, 2, …, n.

17
Q

Define a probability mass function (PMF)

A

pX (x) = P(X = x),
which equals 0 for any x /∈ Dx

18
Q

Define standard deviation

A

For a discrete random variable X:

σX = root(Var[X])

19
Q

Define coefficient of variation

A

Ratio between standard deviation and the mean

CVx = φ = σ/μ

20
Q

Define a binomial distribution

A

X ~ Bin(n,p) , for k successes in n trials has a PMF

P(X = k) =

n
k

 pk(1 − p)n−k

21
Q

Define correlation coefficient

A

ρXY is a standardised measure of dependence between two random variables X and Y

ρXY = Cov[X, Y ]/(σX σY) (-1≤ρXY≤1)

22
Q

Define the sample median

A

Q50, Central value of the ordered data set

Q50 = x (n+1/2)
for n is odd

Q50 = ((x n/2) + (x n/2 +1))/2
for n is even

23
Q

Define the range of an ordered set

A

The range of an ordered set {x1, x2, …, xn} with xi ≤ xj for i < j is
defined as

R(X) = xn − x1.

24
Q

Define the sample mean

A

Sum of all the values divided by how many there are

25
Define the sample variance
Sum of all the values differences from the mean squared divided by how many there are
26
Define interquartile range
Difference between the upper quartile and lower quartile (middle 50%) Q75-Q25
27
Define reliability
Probabilistic relationship between stress and resistance (stress/strain or demand/capacity). That is, reliability is solving the difference of stress and resistance
28
Define the Hasofer-lind reliability index, β
Number of standard deviations the mean is away from failure β = μ/σ
29
Define the design point
Point of failure that is closest to the origin in the standard normal space
30
Define a series system
Entire system fails if any component of the system fails
31
Define a parallel system
Entire system fails if all components of the system fails