Consider the function ρ(y) = log(1 + y 2 ), y ∈ R, and define h(t) as in XXXXXXXXXXAssume that the distribution function F has a density f, symmetric about 0, such that f has heavy tails [i.e., f(x)...

Consider the function ρ(y) = log(1 + y 2 ), y ∈ R, and define h(t) as in (5.21). Assume that the distribution function F has a density f, symmetric about 0, such that f has heavy tails [i.e., f(x) converges to 0 as x → ∞ at a rate slower than the normal or exponential pdf.] Show then that h(t) = 0 may not have a unique minimum at t = 0.