AP Stats: Chapter 6.1

random variable

takes random variables determined by the outcome of a chance process

probability distribution

gives random variables possible values and their probabilities

discrete and continous

two types of random variables

discrete random variable

has a fixed set of possible values with gaps between them

continuous random variable

can take any value in an interval on the number line

mean of a random variable μX

the balance point of the probability distribution histogram or density

standard deviation of a random variable σX

measures how much the values of the variable typically vary from the mean

variance of X

the “average” squared deviation of the values of the variable from their mean

expected value

long run average value of the variable after many repetitions of the chance process, E(X)

how to define shape of a probability distribution histogram or density curve

identifying symmetry or skewness and any major peaks

standard deviation of X

square root of the variance

probability of any event

the sum of all the probabilities of all the values that make up the event

horizontal

axis the values of the variable go on a graph

vertical

axis the probabilities go on a graph

mean

measure of center in a probability distribution

0 and 1

values that probability must fall between

1

area underneath a valid probability density curve for a continuous random variable

probability for any event

the area under the density curve directly above the values on the horizontal axis that make up the event

standard deviation

use this to summarize the variability of a probability distribution

1

sum of all the probabilities in a probability diatribution