An article in the Journal of Database Management [“Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools” (2005, Vol. 16, pp. 1–20)] provided the workload used in the TPC-C OLTP (Transaction Processing Performance Council’s Version C On-Line Transaction Processing) benchmark, which simulates a typical order entry application. See the following table. The frequency of each type of transaction (in the second column) can be used as the percentage of each type of transaction. Let X and Y denote the average number of selects and updates operations, respectively, required for each type transaction. Determine the following:

(a) P(X <5) 

(b) E(X)

(c) Conditional probability mass function of X given Y = 0

(d) P(X <6 |Y = 0) 

(e) E(X |Y = 0)