Math Is Fun Forum

Goldmar

Guest

Probability

I have to show that φ''_X(0) = -variance(X).

I'm aware that the characteristic function is

φ_X(t) = Σ_[n=0] P(X=n)e^(itn)

so the problem just amounts to finding the second derivative at 0 of the above expression. 

However, I'm uncertain as to how to find the second derivative of this (given the crazy notation)...if anyone could give me a push in the right direction, it would be much appreciated!