The inequality
f(tx1 + (1−t)x2) ≤ tf(x1) + (1−t)f(x2)
for a convex ( = concave up) function f and 0 ≤ t ≤ 1. This implies that the chord connecting the points (x1,f(x1)) and (x2,f(x2)) lies above the graph y = f(x) for the interval x1 ≤ x ≤ x2. In probability, the inequality is commonly expressed as f(E(X))≤E(f(X)) where X is a random variable.