5.3 Continuous random variables 67 following sense. If x is small and positive, then, roughly speaking, the probability that X is near x satisfies P(x

5.3 Continuous random variables 67 following sense. If δx is small and positive, then, roughly speaking, the probability that X is

‘near’ x satisfies P(x < X ≤ x + δx) = F(x + δx) − F(x) by (5.10)

=

Z x+δx x

fX (u) du by (5.21)

≈ fX (x)δx for small δx. (5.26)