Chapter 6 Discrete Probability Distributions Flashcards
Random variable
a numerical measure of the outcome from a probability experiment, so its value is determined by chance. Denoted using letters such as X.
Probability
deals with experiments that yield random short-term results yet reveal long-term predictability.
Outcome
The result of a probability experiment.
Law of Large Numbers
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.
Experiment
Any process with uncertain results (or outcomes) that can be repeated.
Sample Space
The collection of all possible outcomes of a probability experiment. Often denoted, S.
Event
Any collection of outcomes from a probability experiment. Consists of one outcome or more than one outcome. Denoted using capital letters, such as E.
Probability Model
A list of the possible outcomes of a probability experiment and each outcome’s probability.
Rules of Probability
1) The probability of the event must be greater than or equal to 0 and less than or equal to 1.
2) The sum of the probabilities of all outcomes must
equal 1.
Impossible Event
An event whose probability is 0.
Certainty
Am event whose probability is 1.
Unusual Event
An event that has a low probability of occurring. Typically, an event with a probability less than 0.05.
Equally Likely Outcomes
Each outcome in a probability experiment has the same probability of occurring.
Tree Diagram
A diagram used to determine the sample space of a probability experiment.
Subjective Probability
The probability of an outcome determined by personal judgement.
Disjoint Events
Two events that have no outcomes in common.
Mutually Exclusive
Another name for disjoint.
Venn Diagram
Events are represented as circles enclosed in a rectangle.
Contingency Table
A table that relates two categories of data.
Two-Way Table
Another name for a contingency table.
Row Variable
The variable that describes each row in the contingency table.
Column Variable
The variable that describes each column in the contingency table.
Cell
The entry in the contingency table where the value of the row variable and column variable intersect.
Complement
Let E denote some event. The complement of E, denoted E^c, are all outcomes in the sample space that are not outcomes in event E.
Independent
Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F.
Dependent Events
Two events E and F are dependent if the occurrence of event E in a probability experiment affects the probability of event F.
Conditional Probability
The probability that some event F occurs, given that some other event, E, has occurred. Denoted P(F|E).
Factorial Symbol
The symbol, denoted n!, where n is greater than or equal to 0 is an integer. The notation is defined as (1) n! = n(n-1) … 321, (2) 0! = 1, and (3) 1! = 1.
Permutation
An ordered arrangement in which r objects are chosen from n distinct (different) objects so that r less than or equal to n and repetition is not allowed. The symbol n^Pr represents the number of permutations of r objects selected from n objects.
Combination
A collection without regard to order, in which r objects are chosen from n distinct objects with r less than or equal to n and without repetition. The symbol n^Cr represents the number of combinations of n distinct objects taken r at a time.
Discrete Random Variable
A variable that has either a finite or countable number of values. The values of a discrete random variable can be plotted on a real number line with space between each point.
Continuous Random Variable
A variable that has infinitely many values. The values of a continuous random variable can be plotted on a real number line in an uninterrupted fashion.
Probability Distribution
Provides the possible values of the random variable X and their corresponding probabilities. A probability distribution can be in the form of a table, graph, or mathematical formula.
Probability Histogram
A histogram in which the horizontal axis corresponds to the value of the random variable and the vertical axis represents the probability of that value of the random variable.
Criteria for a Binomial Probability Experiment
An experiment is said to be a binomial experiment if:
- The experiment is performed a fixed number of times. Each repetition of the experiment is called a trial.
- The trials are independent. This means the outcome of one trial will not affect the outcome of the other trials.
- For each trial, there are two mutually exclusive (or disjoint) outcomes, success or failure.
- The probability of success is fixed for each trial of the experiment.
Excel Format for the BINOM.DIST Function
=BINOM.DIST (no. of successes (x), no. of trials (n), probability of success (p), TRUE or FALSE)
Type FALSE when computing EXACTLY a certain number of successes; type TRUE when computing UP TO and INCLUDING (i.e., accumulating) a certain number of successes.
