Density functions serve continuous random variables in very much the same way as mass functions serve discrete randomvariables, and it is not surprising that the general properties of density functions and mass functions are very similar. For example, it is clear that the density function fX of X satisfies fX (x) ≥ 0 for x ∈ R, (pY (x) ≥ 0) (5.24)

Z

∞

−∞

fX (x) dx = 1,

X x

pY (x) = 1



, (5.25)