A data warehouse of a train company contains information about train segments. It consists of six dimensions, namely, departure station, arrival station, trip, train, arrival time, and departure time, and three measures, namely, number of passengers, duration, and number of kilometers. Write the OLAP queries using window functions along with ROLLUP AND CUBE operations to be performed in order to answer the following questions. Propose dimension hierarchies when needed.

a. Total number of kilometers made by Alstom trains during 2012 departing from French or Belgian stations.

b. Total duration of international trips during 2012, that is, trips departing from a station located in a country and arriving at a station located in another country.

c. Total number of trips that departed from or arrived at Paris during July 2012.

d. Average duration of train segments in Belgium in 2012. e. For each trip, average number of passengers per segment, that is, take all the segments of each trip, and average the number of passengers.