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What is the unity/interpretation of the y-axis of a density distribution function? The X-axis is the values of the random variable, the area is the probabilty what about the y-axis ?

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The y-value is meaning-less for interpretation. As f(x) is probability distribution function and probability being defined as: $P(x<X)=\int_{-\infty}^b\!f(x)dx$. Y-value just has mathematical usage but no physical interpretation. Can refer to the link as well.

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