Probability/ Statistics
Correlation Coefficient
A measure of the strength and the direction of a linear relationship between two variables. The symbol r represents this
Permutation
An ordered arrangement of objects.
Negative Correlatios
As the x increases, the y tends to decrease
Positive Correlations
As the x increases, the y tends to increase
Discrete
It has a finite or countable number of possible outcomes that can be listed
Continuous
It has an uncountable number of possible outcomes represented by an interval on the number line
Probability Distribution
Lists each possible value the random variable can assume, together with its prbability. It must satisfy the following conditions: 0<P(X)<1 EP (X)= 1
Factorial
N!
Distinguishable Permutations
N!/n1!x n2! x n3!...nk! Where n1+n2+n3+....nk+n
Subjective probability
Result from intuition, education guesses, and estimates
Regression Line/Line of Best Fit
The line for which the sum of the square of the residuals is a minimum
Independent Events
The occurrence of one of the events does not affect the probability of the occurrence of the other event
The Addition Rule
The probability that events A or B will occur, P (A or B) is given by: P (A or B)= P (A) + P (B)- P(A and B), Mutually Exclusive: P (A or B)= P (A) + P(B)
The Multiplication Rule
The probability that two events A and B will occur in sequence is: P (A and B)= P(A) x P(B/A). If independent: P (A and B)= P(A) x P(B)
Mutually Exclusive Events
Two events are mutually exclusive if they can't occur at the same time
Independent Variable
X value
Dependent Variable
Y value
event
a subset of the sample space. It may consist of one or more outcomes.
probability experiment
an action, or trial, through which specific results (counts, measurements, or responses) are obtained
simple event
an event that consists of a single outcome
Law of Large Numbers
as an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of an event
Empirical probability
based on observations obtained from probability experiment
fundamental counting principle
if one event can occur in "m" ways and a second event can occur in "n" ways the number of ways the two events can occur in sequence is m x n
Combinations
is a selection of r objects from a group of n objects without regard to order and is denoted by nCr.
Combinations
nCr= n!/r!(n-r)!
Permutation
nPr=n!/(n-r)! where r < n
Dependent Events
one event affects the probability of the other event occurring
range of probabilities
probability of an event E is between 0 and 1 inclusive 0<P(x)<1
Conditional Probabilty
probability of an event occurring, given that another event has already occurred. P(B/A)
Correlation
realtionship b/w two variables
Random variable
represents a numerical value associated with each outcome of a probability experiment
Scatter Plot
the graph of ordered pairs
probability
the likelihood that an event will occur
outcome
the result of a single trail in a probability experiment
Expected Vaule
the same value as the mean and average
Complement of an Event
the set of all outcomes in a sample space that are not included in event E. P(E')
sample space
the set of all possible outcomes of a probability experiment
Classical probability
used when each outcome in a sample space is equally likely to occur