Chapter 13: Randomness and Probability Flashcards
Random Process
Generates results that are determined by chance; Aware of possible outcomes, but have no idea what the outcome will be; Even though individual outcomes are uncertain, there is a sense of predictability that occurs in the long run; Patterns of random occurences may include strings or runs of outcomes that appear to be non-random
Outcome
Result of a trial of a random process
Event
Collection of outcomes
Law Of Large Numbers
After many trials, simulated probabilities get closer to the true probability as the number of trials increases (gets infinitely large)
Sample Spaces
The sets of all possible non-overlapping outcomes
Probability Of An Event
Will always be a number between 0 and 1, inclusive
Relative Frequency
Probability of events in repeatable situations can be interpreted as the relative frequency with which the event will occur in the long run
Evidence For A Claim
Assuming a claim is true, find the probability of getting the observed result or more extreme. If < α, then we don’t have convincing evidence against the claim (statistically significant)
Complements
The complement of an event A is the event that A doesn’t happen; A^c; 1-P(A)=P(A^c)
Experimental Probability
Chance of an event occurring based on experiment
Theoretical Probability
Chance of an event occurring based on reasoning/math
Venn Diagrams
Used to represent probabilities in visual form; often use circles/ovals to represent events; the portion where the graphs overlap is the intersection of the two events
A∩B
Probability of event A and event B
A∪B
Probability of event A or event B
Mutually Exclusive Events
Events that can’t occur at the same time; no intersection
Conditional Probability (B|A)
Read as “B given A”; probability that event B will occur given that event A has occurred
P(B|A)=P(A∩B)/P(A)
Independent Events
Knowing whether or not one event has occurred (or will occur) does not change that probability that another event will occur
P(A|B)=P(A) and P(A|B^c)=P(A)
General Multiplication Rule
(Only when independent) P(A∩B)=P(A)*P(B)
