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Random Variable

A random variable X is a rule that assigns a numerical value to each outcome in

the sample space of an experiment.

A discrete random variable can take on specific, isolated numerical values, like

the outcome of a roll of a die, or the number of dollars in a randomly chosen

bank account.

A continuous random variable can take on any values within a continuum or an

interval, like the temperature in Central Park, or the height of an athlete in

centimeters.

Discrete random variables that can take on only finitely many values (like the

outcome of a roll of a die) are called finite random variables.

Probability Distribution

The probability P(X = x) is the probability of the event that X = x. Similarly,

the probability that P(a