Imagine there is a 6 sided die with sides 1, 4, 9, 16, 25 and 36. The die is not fair, which means that the sides do not have the same probability of turning up. The first three sides (1, 4, 9) have only 10% of chance of turning up, while the last three (16, 25, 36) have 20%, 30% and 20% respectively. Calculate the variance of the random variable that models the outcome of the die.