# Mean and Variance of a Discrete Random Variable

3.39 If the range of X is the set {0,1,2,3,4} and P(X = x) = 0.2 determine the mean and variance of the random variable.

3.47 The range of the random variable X is [0,1,2,3,x], where x is unknown. If each value is equally likely and the mean of X is 6, determine x.

3.49 The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the right is appropriate is 0.0001. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. What is the mean and variance of X?

3.51 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-COLTP (Transaction Processing Performance Council's Version C On-Line Transaction Processing) benchmark, which simulates a typical order entry application.

The frequency of each type of transaction (in the second column) can be used as the percentage of each type of transaction. The average number of selects operations required for each type of transaction is shown.

a) Determine the mean and standard deviation of the number of select operations for a transaction from the distribution of types shown in the table.

b) Determine the mean and standard deviation of the total number of operations (selects, updates, ... and joins) for a transaction from the distribution of types shown in the table.

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#### Solution Summary

The mean and variance of a discrete random variable is given. The range of the random variable is determined.