Symbols
What is P(E)?
The probability of an event to occur.
What is a Null Event?
An event with no outcomes (impossible).
Define Probability
How likely an outcome is to occur out of all possible outcomes.
What is the "mean" of a data set?
The average of a data set.
Which of the following is an example of probability and statistics used in engineering?
A) Predicting how large the next earthquake’s magnitude will be
B) Calculating how many 2x4s are needed to construct a building
A) Predicting how large the next earthquake’s magnitude will be
What do the following symbols represent:
P(A∪B) and P(A∩B)
Union representing A "or" B and Intersection representing A "and" B.
Two events that cannot happen at the same time.
Define Conditional Probability
The probability that an event occurs given that another event has already occurred.
The middle value in an ordered data set.
A factory produces bolts for buildings where 2% are defective. If one bolt is selected at random, what is the probability it is NOT defective?
0.98
What is P(A|B)?
The probability that A occurs given that B has already occurred.
What are Collectively Exhaustive events?
Events that if together include every possible outcome.
Define Sample Space
What is the "mode" of a data set?
What is the most frequently occurring value in a data set.
A sensor on a bridge triggered an alarm, a bridge engineer computes the probability that damage actually exists using ______ type of probability.
Conditional Probability
What is P(A|B) = P(B|A)P(A) / P(B)
Bayes' Theorem
How is the Bayesian Probability interpreted?
How confident we are based on what we know.
Define Aleatory
Natural randomness
What value represents the square root of the variance?
The Standard Deviation
An engineer calculates the overall probability of system failure by adding probabilities from all possible failures using what probability law.
The Law of Total Probability
What is P(F∪S)=P(F)+P(S)-P(F∩S)
How is Frequentist Probability interpreted?
How often over many repeated trials an event occurs.
Define Epistemic
Imperfect modeling and estimation.
What is the difference between the maximum and minimum values?
The Range
This theorem allows engineers to update probabilities when new information becomes available.
Bayes' Theorem