Definitions

Question 1

Define Risk Analysis

Answer 1

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

Question 2

Define Risk Measure

Answer 2

Product of probability of occurrence and its consequences:

R = P(E)*Ce

Question 3

What are the three axioms of probability?

Answer 3

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)

Question 4

Define a Random Experiment/Trial

Answer 4

Process that may provide different outcomes when observed repeatedly

Question 5

Define Outcome

Answer 5

Each particular possible result off a trial

Question 6

Define sample space and empty space

Answer 6

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

∅, set of no events

Question 7

Define Event

Answer 7

Set of outcomes

Question 8

Define De Morgan rule

Answer 8

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)

Question 9

Define probability measure and triplet

Answer 9

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).

Question 10

Define Conditional probability

Answer 10

Event A occurs given B has occurred

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

Question 11

Define independence

Answer 11

One event does not influence the other

P(A|B) = P(A)

Question 12

Define Bayes Theorem

Answer 12

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

Question 13

Define a random variable

Answer 13

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

Question 14

Define a discrete random variable

Answer 14

Random variable that is finite or countably infinite

Question 15

Define a continuous random variable

Answer 15

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

Question 16

Define a probability distribution

Answer 16

Probability X takes a particular value

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

Question 17

Define a probability mass function (PMF)

Answer 17

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

Question 18

Define standard deviation

Answer 18

For a discrete random variable X:

σX = root(Var[X])

Question 19

Define coefficient of variation

Answer 19

Ratio between standard deviation and the mean

CVx = φ = σ/μ

Question 20

Define a binomial distribution

Answer 20

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

P(X = k) =

n
k

 pk(1 − p)n−k

Question 21

Define correlation coefficient

Answer 21

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

ρXY = Cov[X, Y ]/(σX σY) (-1≤ρXY≤1)

Question 22

Define the sample median

Answer 22

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

Question 23

Define the range of an ordered set

Answer 23

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

R(X) = xn − x1.

Question 24

Define the sample mean

Answer 24

Sum of all the values divided by how many there are

Question 25

Define the sample variance

Answer 25

Sum of all the values differences from the mean squared divided by how many there are

Question 26

Define interquartile range

Answer 26

Difference between the upper quartile and lower quartile (middle 50%)

Q75-Q25

Question 27

Define reliability

Answer 27

Probabilistic relationship between stress and resistance (stress/strain or demand/capacity).

That is, reliability is solving the difference of stress and resistance

Question 28

Define the Hasofer-lind reliability index, β

Answer 28

Number of standard deviations the mean is away from failure

β = μ/σ

Question 29

Define the design point

Answer 29

Point of failure that is closest to the origin in the standard normal space

Question 30

Define a series system

Answer 30

Entire system fails if any component of the system fails

Question 31

Define a parallel system

Answer 31

Entire system fails if all components of the system fails