lesson
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Imagine tossing three fair coins. You do not just care about heads or tails — you want to count the exact number of heads you get.
A rule that turns random outcomes into numerical values is called a random variable.
Discrete Random Variables
A discrete random variable is a variable whose possible values are separate, distinct numbers that you can list or count.
We write uppercase X to represent the variable itself, and lowercase x for a specific numerical value it can take.
📊Interactive diagram
How do we display every single value X can take alongside its exact probability?
Probability Distribution Tables
A probability mass function (often written P(X=x)) gives the probability that X takes the exact value x.
We summarize the full set of outcomes in a clean layout known as a probability distribution.
📊Interactive diagram
Is there an absolute mathematical law that every valid probability distribution must obey?