Unit 6: Anticipating Patterns

Disjoint

or mutually exclusive events: events that have no outcome in common.

Complement

: the set of all possible outcomes in a sample space that do not lead to the event.

Intersection

: events A and B is the set of all possible outcomes that lead to both events A and B.

Parameter

: a numerical measurement describing some characteristic of a population.

Central limit theorem

: If the sample size is large enough then we can assume it has an approximately normal distribution.

n trials

The are independent and are repeated using identical conditions.

sample size

The has to be greater than 30 to assume an approximately normal distribution.

Tree diagram

: representation is useful in determining the sample space for an experiment, especially if there are relatively few possible outcomes.

Standard deviation

is the of the original distribution.

Standard deviation

is the of the original distribution.

B

Union: events A and is the set of all possible outcomes that lead to at least one of the two events A and .

original distribution

Mean is the mean of the .

original distribution

Mean is the mean of the .

Sample space

: a set of all possible outcomes.

Standard error

: standard deviation of the distribution of the statistics.

original distribution

Mean is the mean of the .

Statistic

: a numerical measurement describing some characteristic of a sample.

Probability

the chance of the outcome of an event

Sample space

a set of all possible outcomes

Tree diagram

representation is useful in determining the sample space for an experiment, especially if there are relatively few possible outcomes

Rule 1

For any event A, the probability of A is always greater than or equal to 0 and less than or equal to 1

Rule 2

The sum of the probabilities for all possible outcomes in a sample space is always 1

Impossible event

If an event can never occur, its probability is 0

Sure event

Of an event must occur every time, its probability is 1

"Odds in favor of an event"

ratio of the probability of the occurrence of an event to the probability of the nonoccurrence of that event

Complement

the set of all possible outcomes in a sample space that do not lead to the event

Disjoint or mutually exclusive events

events that have no outcome in common

Union

events A and B is the set of all possible outcomes that lead to at least one of the two events A and B

Intersection

events A and B is the set of all possible outcomes that lead to both events A and B

Conditional Events

A given B is a set of outcomes for event A that occurs if B has occurred

Variable

quantity whose value varies from subject to subject

Probability experiment

an experiment whose possible outcomes may be known but whose exact outcome is a random event and cannot be predicted with certainty in advance

Random variables

The outcome of a probability experiment takes a numerical value

Discrete random variable

quantitative variable that takes a countable number of values

Continuous random variable

a quantitative variable that can take all the possible values in a given range

Expected value

Computed by multiplying each value of the random variable by its probability and then adding over the sample space

Variance

sum of the product of squared deviation of the values of the variable from the mean and the corresponding probabilities

Combination

the number of ways r items can be selected out of n items if the order of selection is not important

The continuous probability distribution (cdf)

graph or a formula giving all possible values taken by a random variable and the corresponding probabilities

Parameter

a numerical measurement describing some characteristic of a population

Statistic

a numerical measurement describing some characteristic of a sample

Sampling distribution

the probability distribution of all possible values of a statistic, different samples of the same size from the same population will result in different statistical values

Standard error

standard deviation of the distribution of the statistics

Central limit theorem

If the sample size is large enough then we can assume it has an approximately normal distribution

Mean

μ = 1/p

Standard Deviation

σ = √1/𝑝(1/𝑝−1)