Let X1,...,Xn be i.i.d. random variables with a density function where f is symmetric about 0. Let then (i) What is the asymptotic variance of (ii) Under what condition on f , does it have a...

Let X₁,...,X_n
be i.i.d. random variables with a density function

where f is symmetric about 0. Let then

(i) What is the asymptotic variance of

(ii) Under what condition on f , does it have a minimum at p = 1/2?

(iii) Verify (ii) when f is (a) normal and (b) double exponential.