Chapter 4: Probability Concepts Flashcards
Probability Theory is the science of ______. It allows you to evaluate and control the likelihood an inferential statistic is correct.
uncertainty
When outcomes are equally likely, the probability of an event is equal to the ________
relative frequency
What is the freqentist interpretation of probability
The probability of an event is the proportion of times it occurs in a large number of repetitions of an experiment
____ is a mathematical description of the experiment based on certain primary aspects and assumptions
Probability model
What is the primary aspect and assumption of the equal-likelihood model
All possible outcomes are equally likely to occur
Name for an event with a probability of 0
impossible event
Name for an event with a probability of 1
certain event
The collection of all possible outcomes of an experiment is called the _____
sample space
An ______ is a collection of outcomes for the experiment that is a subset of the sample space. It _____ if the outcome of the experiment is a member of the subset.
Event, occurs
Events and relationships among events can be easily visualized using ______
Venn diagrams
Express the event “E does not occur”
(not E)
Express the event both A and B occur
(A & B)
Express the event both A or B or both occur
(A or B)
Two or more events are _______ if no two share outcomes in common
Mutually Exclusive Events
P(E) represent ______
The probability of E in probability notation
The special addition rule can only be used if events are __________
mutually exclusive
The complement of an event E
(not E)
In the general addition rule, you ______ doubly counted shared events from the sum
subtract out
Data from one variable of a population is called _____. From two variables is called ______.
univariate data, bivariate data
The frequency distribution for bivariate data is called a ______
contingency table/two-way table
Joint probabilities describe joint events, and are ___ in a joint probability distribution
cells
Marginal probabilities correspond to a single event and are found in the ____ of a contingency table
margin (end of row/column)
Express the conditional probability that event B occurs given that event A occurs: _____ A is the _____ event.
P(B|A), given
A ____ can be used to visualize the general multiplication rule
tree diagram
If P(B|A) = P(B) an event B is _____ of event A
independent
If event B is independent of event A, event A is also independent of event B. A and B are _____
independent events
If P(A&B) != P(A) * P(B), B and A are ______
dependent events
Events are ______ events if one or more of them must occur
exhaustive
An event and its ______ are mutually exclusive and exhaustive
complement
The rule of total probability is also referred to as ____
the stratified sampling theorem
In Bayesian statistical inference, the probability of an event before new data is collected is called _____
prior probability
In Bayesian statistics, the revised or updated probability of an event occurring after taking into consideration new information is called ______
posterior probability
Techniques that do not rely on a direct listing for determining the number of ways something can happen
Counting rules
The ______ assumes sequential actions each with a defined number of possibilities and multiplies together the possibilities of all actions to find total possible outcomes
Basic Counting Rule
_____ is the product of the first k positive integers
k factorial, denoted k!
A ______ of r objects from a collection of m objects is any ordered arrangement of r of the m objects
permutation
mPr (read “m permute r”) denotes what?
The number of possible permutations of r objects that can be formed from a collection of m objects
The number of possible permutations of m objects among themselves is __. This is called the ______.
m!, special permutations rule
A _____ of r objects from a collection of m objects is any unordered arrangement of r of the m objects – any subset of r objects from a collection of m objects.
combination
What is denoted by mCr (read “m choose r”)
The number of possible combinations of r objects formed from a collection of m objects
T/F There will be more combinations than permutations given a set of r objects from a collection of m objects
False, the number of combinations will be the number of permutations divided by the number of possible permutations of r objects among themselves
Express the number of possible samples of a size n from a population of size N as a combination
NCn
