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