Chapter 5 Flashcards
Simulation
The imitation of chance behavior, based on a model that accurately reflects the situation
Performing a simulation
- State: ask a question of interest about some chance process
- Plan: describe how to use a chance device to imitate one repetition of the process, tell what you will record at the end of each repetition
- Do: perform many repetitions
- Conclude: use the results of your simulation to answer the question
Law of large numbers
If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value
Probability
A value between 0-1 that describes the oportion of times an outcome would occur in a very long series of repetitions
The myth of short-run regularity
Our intuition tries to tell us that random phenomena should be predictable in the short-run, but probability does not allow use to make short-run prediction because probability is the idea that randomness is predictable in the long-run
The myth of the “law of averages”
Past outcomes do not influence the likelihood of individual outcomes in the future
Sample space
The set of all possible outcomes
Probability model
A description of some chance process that consists of two parts:
* A sample space, S
* A probability for each outcome
Event
- Any collection of outcomes from some chance process
- Designated by a capital letter (A, B, C, etc.)
Complement rule
The probability that an event doesn’t occur is 1 minus the probability of the event does occur
Addition rule
P(A or B) = P(A) + P(B) - P(A and B)
Multiplication rule
General: P(A and B) = P(A | B) * P(B)
For individual events: P(A and B) = P(A) * P(B)
Conditional probability
The probability that one event happens given that another event is already known to happen
Conditional probability P(A | B)
P(A | B) = P(A and B) / P(B)
Conditional probability P(B | A)
P(B | A) = P(B and A) / P(A)
