Continuous Random Variables

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A continuous random variable maps outcomes to values of an uncountable set (e.g., the real numbers). For a continuous random variable, the probability of any specific value is zero, whereas the probability of some infinite set of values (such as an interval of non-zero length) may be positive.

Basic Definition

Cumulative distribution function for a continuous random variable X with a numerical value of interest a is

Key Variables


Standardized Random Variable


Normal Distribution

Probability Density Function

Jointly Distributed Continuous Random Variable