Definitions Flashcards
Define Risk Analysis
Provides a framework and computational tools for assessing the safety of systems and follow up decision making
Define Risk Measure
Product of probability of occurrence and its consequences:
R = P(E)*Ce
What are the three axioms of probability?
- For every event, E, P(E)≥0
- Probability of all events, S, P(S)=1
- For mutually exclusive events: P(AuB)=P(A)+P(B)
Define a Random Experiment/Trial
Process that may provide different outcomes when observed repeatedly
Define Outcome
Each particular possible result off a trial
Define sample space and empty space
S or Ω, set of all possible outcomes of the trial
∅, set of no events
Define Event
Set of outcomes
Define De Morgan rule
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)
Define probability measure and triplet
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).
Define Conditional probability
Event A occurs given B has occurred
P(A|B) = P(A ∩ B)/P(B) , provided P(B) doesn’t equal 0
Define independence
One event does not influence the other
P(A|B) = P(A)
Define Bayes Theorem
P(B|A) = (P(A|B)P(B))/P(A)
Define a random variable
Mathematical tool for describing an event, maps the the possible outcomes of an event to a number line
Define a discrete random variable
Random variable that is finite or countably infinite
Define a continuous random variable
Random variable that is an interval of R or a union of intervals
Define a probability distribution
Probability X takes a particular value
pk = pX (xk) = P(X = xk) = P({w ∈ Ω|x(w) = xk}), k = 1, 2, …, n.
Define a probability mass function (PMF)
pX (x) = P(X = x),
which equals 0 for any x /∈ Dx
Define standard deviation
For a discrete random variable X:
σX = root(Var[X])
Define coefficient of variation
Ratio between standard deviation and the mean
CVx = φ = σ/μ
Define a binomial distribution
X ~ Bin(n,p) , for k successes in n trials has a PMF
P(X = k) =
n
k
pk(1 − p)n−k
Define correlation coefficient
ρXY is a standardised measure of dependence between two random variables X and Y
ρXY = Cov[X, Y ]/(σX σY) (-1≤ρXY≤1)
Define the sample median
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
Define the range of an ordered set
The range of an ordered set {x1, x2, …, xn} with xi ≤ xj for i < j is
defined as
R(X) = xn − x1.
Define the sample mean
Sum of all the values divided by how many there are
Define the sample variance
Sum of all the values differences from the mean squared divided by how many there are
Define interquartile range
Difference between the upper quartile and lower quartile (middle 50%)
Q75-Q25
Define reliability
Probabilistic relationship between stress and resistance (stress/strain or demand/capacity).
That is, reliability is solving the difference of stress and resistance
Define the Hasofer-lind reliability index, β
Number of standard deviations the mean is away from failure
β = μ/σ
Define the design point
Point of failure that is closest to the origin in the standard normal space
Define a series system
Entire system fails if any component of the system fails
Define a parallel system
Entire system fails if all components of the system fails
