Lecture 2
Discrete Random VariablesSection 2.1-2.4
Definition
• Each observation of an experiment is a random variable. (e.g. X)
• The set of possible values of a random variable is called the range of a random variable. (e.g. SX)
• A random variable can be a function of the observation.
• A random variable can be a function of another random variable
• English translation: {X=x} emphasizes the idea that there is a set of sample points s within S (the sample space) for which X(s)=x.
Probability Mass Function
Probability Mass Function
Families of Discrete Random Variables
• Bernoulli Random Variable• Geometric Random Variable• Binomial Random Variable• Pascal Random Variable• Discrete Uniform Random Variable (Not
Covered)• Poisson Random Variable
Bernoulli Random Variable
Examples of a Bernoulli Random Variable (1)
bernoullipmf(p,x)
Geometric Random Variable
Geometric RV Example (1)
geometricpmf(p,x)
Binomial Random Variable
Binomial RV Example (1)
binomialpmf(n,p,x)
Pascal Random Variable
Pascal Random Variable Example
Poisson Random Variable
An Example of Poisson Random Variable
poinsonpmf(alpha,x)
An Example of Poisson Random Variable
An Example of Poisson Random Variable
An Example of Poisson Random Variable
geometricdf(p,x)
What is the probability that Y is greater than 3?
poissoncdf(alpha,x)
What is the probability that the switching office receives more than 2 calls, butless than 10 calls?