
Discrete random variable
A discrete random variable is a random variable that can take on only a finite or at most a countably infinite number of values

Basic description of the probability mass function:
function p such that
and

cumulative distribution function (cdf)

Random variable
a numeric outcome from a random problem

support
The values a random variable can take on is the support of a variable

The probability of k successes in a binomial distribution:

Probability of all the variation of successful sequences in a binomial distribution

Use of capital and lower case letters to describe random variables and their realizations
 capital= random variable possibilities
 lowercase= realization (set of finite/interval of values)

Continuous random variables
has an interval or union of intervals as its support

distribution
pattern and frequency we observe the random variable

Formula for a geometric distribution

Formula for a negative binomial distribution


What do you get when you take the integral of a PDF?
probability!

Endpoints don't matter if you are finding probabilities for continuous functions
T/F
True

How do you find probability from a PMF?
 sum of the range it has support for
 (discrete)

How do you find probability for a PDF?
Integrate over the range of interest

Endpoints don't matter for a PMF
T/F
False

What are values of the PDF often refered to as?
relative liklihoods

(graph)

(graph)

(graph)

(graph)

In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: population
all coins of this type

In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: parameter
=p= P(coin lands on heads)

In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: sample
Sequence of observed coin flips

In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: Statistic
observed number of heads (y) or sample proportion of heads

Support
values the random variables can take on

The differences between CAPITAL and lowercase variables
ex. X vs x
little 'x' represents realization of the random variable
big 'X' represents the actual random variable

Support for a discrete random variable
countable support

Support for a continuous random variable
interval (or union of intervals) for the support

How can you identify a CDF of a random variable Y?

Cumulative Distribution Function (cdf) of a random variable (Y)
denoted as either: or
The cumulative probability up to and including the actualized value of (y)

Graph the CDF and find


Frequency function
The probability mass function of a discrete random variable:


Describe a PDF
PDF is a visualization of the distribution of your random variable


For discrete random variables, the probabilities are the sum of the PMF over the range of interest and (end points do matter)
T/F
True

For continuous random variables, the probabilities are the integrals of the PDF over the range of interest and (end points do matter)
T/F
 False
 End points DO NOT matter

Solving for probability for a discrete variable:
(PMF or PDF? describe how to solve)
PMF

Solving for probability for a continuous variable:
(PMF or PDF? describe how to solve)

integrating factor=
constant required to make an integral = 1

What are the values of the PDF often refered to as?
"relative likelihoods"

Does f(a) or f(b) have a higher liklihood?
f(a)

Formula for finding probability from a CDF:

Formula for finding probability from a PDF:

Formula for finding probability from a PMF:

Expected value for a random variable Y:
 Expected Value (or Mean) of a RV Y , denoted as E(Y)= µY , is the average value of Y weighted by the probability distribution.

