Hello.

Question: Consider a density for the proportion of a person's body that is covered in freckles, X, given by f(x) = cx for 0 <=x<=1 and some constant c.

a. What value of c makes this function a valid density?

b. What is the mean and variance of this density?

c. You simulated 100; 000 sample means, each comprised of 100 draws from this

density. You then took the variance of those 100; 000 numbers. Approximately

what number did you obtain? (Explain.)