Problem 1. OLAP (12 points) We would like to build a data cube of the fruit data, and want to include the following dimensions and measures: - 4 dimensions: (Variety, Location, Size, Maturity) - 3 measures: (Price.mean, Price.min, Fruit.num_eq-min) It indicates that the fruit price is a function of variety, location, size and maturity. Suppose we are aggregating from the Maturity 1-D cuboid to the apex cuboid. The meanings of these measures are explained below. (1) (6 points) Show that Price.mean is an algebraic measure. What distributive measures do you need to use in calculating Price.mean? Here Price.mean denotes the mean value of all prices. (2) (6 points) Explain whether Fruit.num_eq_min is an algebraic measure or holistic measure. Please justify your answer. Here Fruit.num_eq_min means the number of fruits that have the lowest price. For example, given 5 fruits with prices: 10, 11, 23, 10, 23, then the the lowest price is Price.min =10 and Fruit.num_eq_min =2