6) Consider the random variable Z_n = cos(2**Y_n/n) where Yn is binomial(n,p)

a. What is its asymptotic variance for arbitrary p as n increases

b. What happens at p=1/2

c. Write an r program that shows you graphical the (simulated) standard deviation of vs 1/sqrt(n) as n increases for different values of p including 0.5