Random Variables

Discrete Random Variable: A variable that can only take discrete values

Continuous Random Variables: A variable that can table on any value in a certain interval.

Expected Value: The mean of a Random Variable.

Binomial Random Variables

A variable that can take on exactly two values, like a coin flip.

Info

In order for a variable X to be a binomial random variable,

each trial must be independent,
each trial can have only two outcomes - a “success” or “failure,”
there are a fixed number of trials, and
the probability of success on each trial is constant.

These follow the Binomial Distribution. Also see Binomial Probability

Bernoulli Random Variables

A special category of Binomial RV with exactly one trial with possible outcomes {0, 1} where 0 signifies failure and 1 signifies success.

The PMF distrbution for a Bernoulli RV will be the distribution for \(P(X=0)\) and \(P(X=1)\).

Unlike the Binomial RV where we decide the number of trials ahead of time, in case of Geometric RV, we run an infinite number of trials until we get a success. The probablity of success on the nth attempt is given by the Geometric Probability

The other three conditions for the Binomial RV are applicable to Geometric RV as well.

These follow the Geometric Distribution.

Random Variables