# Counterexample of a theorem for characteristic function.

Let $$X$$ be an $$\mathbb R$$-valued random variable and let $$f(t)$$ be his characteristic function. If $$f$$ is derivable up to order $$k$$ in $$t=0$$ , where $$k$$ is even, then $$X$$ has a finite $$k$$-th expectation.

I ask for a counterexample where $$k$$ is not even.

• Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Feb 1 at 9:52
• Have a look at this. – drhab Feb 1 at 10:01
• drhab can you give me an hint to prove that the characteristics function is derivable in 0 ? – Dario La Torre Feb 1 at 10:55