Continuous Random Variable
A continuous random variable X can assume any real value within a specified interval. Probabilities are described by a probability density function (PDF) f(x), where P(a ≤ X ≤ b) equals the area under the curve between a and b, and the total area under the curve equals 1.
Real World
The height of 18-year-old males in the UK follows a continuous distribution — there is no single 'most likely' height, but heights between 175 cm and 180 cm have a calculable probability.
Exam Focus
Never write P(X = a) for a continuous variable; always find probabilities over intervals using integration or the CDF.
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