CONTENTS

Solution: A Jump Integrator as a Point Mass

Exercise: A Jump Integrator as a Point Mass

Solution

The integrator is flat except for a jump of size 33 at x=1x=1. The integral therefore picks up f(1)f(1) times the jump:

∫02x2 dg(x)=12⋅3=3.\int_0^2 x^2\,dg(x)=1^2\cdot3=3.

Takeaways

  • Jumps act like point masses.
  • The size of the jump multiplies the integrand value.
  • This is why Stieltjes notation handles mixed discrete-continuous distributions cleanly.
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