Stat Vocab chapter 5 & partly 6

Geometric setting

A ________ arises when we perform independent trials of the same chance process and record the number of trials until a particular outcome occurs. The four conditions for a geometric setting are: • Binary? The possible outcomes of each trial can be classified as "success" or "failure." • Independent? Trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial. • Trials? The goal is to count the number of trials until the first success occurs. • Success? On each trial, the probability p of success must be the same.

Probability model

A description of some chance process that consists of two parts: a sample space S and a probability for each outcome.

Event

Any collection of outcomes from some chance process. That is, an ________ is a subset of the sample space. ________ are usually designated by capital letters, like A, B, C, and so on.

Multiplication rule for independent events

If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) ∙ P(B).

Independent random variables

If knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone, and vice versa, then X and Y are ________. That is, there is no association between the values of one variable and the values of the other.

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., which we call the probability of that outcome.

Binomial distribution

In a binomial setting, suppose we let X = the number of successes. The probability distribution of X is a binomial distribution with parameters n and p, where n is the number of trials of the chance process and p is the probability of a success on any one trial. The possible values of X are the whole numbers from 0 to n.w

Geometric distribution

In a geometric setting, suppose we let Y = the number of trials required to get the first success. The probability distribution of Y is a ________ with parameter p, the probability of a success on any trial. The possible values of Y are 1, 2, 3, ....

Discrete random variable

Takes a fixed set of possible values with gaps between. The probability distribution of a ________ gives its possible values and their probabilities. The probability of any event is the sum of the probabilities for the values of the variable that make up the event.

Continuous random variable

Takes all values in an interval of numbers. The probability distribution of a ________ is described by a density curve. The probability of any event is the area under the density curve and above the values of the variable that make up the event.

Random Variable

Takes numerical values that describe the outcomes of some chance process.

Probability distribution

The ________ of a random variable gives its possible values and their probabilities.

Probability

The ________ of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions.

Intersection

The ________ of events A and B, denoted by A ∩ B, refers to the situation when both events occur at the same time.

Union

The ________ of events A and B, denoted by A ∪ B, consists of all outcomes in A, or B, or both.

Mean (expected value, E(X)) of a random variable

The ________, denoted by μX, is the balance point of the probability distribution histogram or density curve. Since the mean is the long-run average value of the variable after many repetitions of the chance process, it is also known as the ________.

Variance of a random variable σx^2

The average squared deviation of the values of the variable from their mean.

Binomial random variable

The count X of successes in a binomial setting.

Simulation

The imitation of chance behavior, based on a model that accurately reflects the situation.

Standard deviation of a random variable

The square root of the variance of a random variable σx^2. The ________ measures the variability of the distribution about the mean.

Conditional probability formula

To find the ________ P(B | A), use the formula P(B|A)= P(A∩B) / P(A).

Mutually exclusive (disjoint)

Two events are ________ if they have no outcomes in common and so can never occur together.

Independent events

Two events are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if P(A | B) = P(A) and P(B | A) = P(B).

Tree diagram

Used to display the sample space for a chance process that involves a sequence of outcomes.

Two-way tables and Venn diagrams

Used to display the sample space for a chance process. ________ can also be used to find probabilities involving events A and B.

General addition rule

If A and B are any two events resulting from some chance process, then the probability that event A or event B (or both) occur is P(A∪B)= P(A) + P(B) - P(A∩B).

Binomial setting

Arises when we perform several independent trials of the same chance process and record the number of times that a particular outcome occurs. The four conditions for a ________ are: • Binary? The possible outcomes of each trial can be classified as "success" or "failure." • Independent? Trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial. • Number? The number of trials n of the chance process must be fixed in advance. • Success? On each trial, the probability p of success must be the same.

Complement of an event A^C

Refers to the event "not A".

Geometric random variable

The number of trials Y that it takes to get a success in a geometric setting.

Complement rule

The probability that an event does not occur is 1 minus the probability that the event does occur. In symbols, P(A^C) = 1 - P(A).

General multiplication rule

The probability that events A and B both occur can be found using the formula P(A ∩ B) = P(A) ∙ P(B | A) where P(B | A) is the conditional probability that event B occurs given that event A has already occurred.

Conditional probability

The probability that one event happens given that another event is already known to have happened. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B | A).

Sample space S

The set of all possible outcomes of a chance process.