topic 9 cards

random

of or characterizing a process of selection in which each item of a set has an equal probability of being chosen

probability

the proportion of times the outcome would occur in a very long series of repetitions

independence

the outcome of one trial must not influence the outcome of another

random phenomenon

outcomes that we can not predict but that nonetheless have a regular distribution in very many repetitions

sample space (s)

in a random phenomenon, it is the set of all possible outcomes

event

is an outcome or a set of outcomes of a random phenomenon

disjoint

events A and B have no outcomes in common

independent

when events A and B occur, one event does not change the probability of the other

continuous random variable

a random variable that may assume any numerical value within the range of values. the range may be infinite or bounded at either or both ends

density curve

a curve that is on or above the horizontal axis, and has an area of exactly one underneath it

discrete random variable

a random variable that can take one of a finite number of distinct outcomes

probability distribution

lists the values and their probabilities

probability histogram

a graph of the probability distribution that divides up the range of possible values in a data set into classes or groups

random variable

a variable whose value is a numerical outcome of a random phenomenon (shown by a capital letter, often X)

uniform distribution

a density curve with a height of 1, ranging from 0 to 1

binomial setting

given a fixed number of independent observations and the fact that each observation falls into either "success" or "failure", the probability of success is the same for each observation

binomial random variable

the random variable X = number of successes if the data is produced in a binomial setting

binomial distribution

given parameters n and p, the distribution of the count X of successes in the binomial setting

probability distribution function (PDF)

Assigns a probability to each value of X

Cumulative Distribution Function (CDF)

assigns the sum of probabilities for values less than or equal to X

binomial coefficient

The number of ways of arranging k successes among n observations

Binomial Probability

If X has the binomial distribution with n observation and probability p of success on each observation, the possible values of X are 0, 1, 2, ..., n.

union (u)

of events A and B contains all outcomes in A, in B, or in both A and B

joint event

The simultaneous occurrence of two events

joint probability

the probability of a joint event

conditional probability

gives the probability of one event under the condition that we know another event

intersection (n)

contains all outcomes that are in both A and B, but not outcomes in A or B alone

compliment

of any event A is the event that A does not occur, written as A^c