Definitions Flashcards
(31 cards)
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
