(i) What value of k makes this a valid probability density function: f(x) = kx^2 for 1 < x < 3. Answer to 4 decimal places.
(ii) Using your answer to part (i), what is the mean of X? Answer to THREE decimal places.
(iii) Using your answers to part (i) and (ii), what is the variance of X? Answer to FOUR decimal places.