Average signature and 4-genus of 2-bridge knots

We show that the average or expected absolute value of the signatures of all 2-bridge knots with crossing number c approaches √2c/π. Baader, Kjuchukova, Lewark, Misev, and Ray consider a model for 2-bridge knot diagrams indexed by diagrammatic crossing number n and show that the average 4-genus is sublinear in n. We build upon this result in two ways to obtain an upper bound for the average 4-genus of a 2-bridge knot: our model is indexed by crossing number c and gives a specific sublinear upper bound of 9.75c/log c.