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

Pascalpmf(k,p,x)

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

CDF

CDF Example

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?