For the Transaction Processing Performance Council’s

Chapter 5, Problem 11E

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QUESTION:

For the Transaction Processing Performance Council’s benchmark in Exercise 5-10, let X, Y , and Z denote the average number of selects, updates, and inserts operations required for each type of transaction, respectively. Calculate the following:

(a) \(f_{x y z}(x, y, z)\)

(b) Conditional probability mass function for X and Y given Z = 0

(c) \(P(X<6, Y<6 \mid Z=0)\)

(d) \(E(X \mid Y=0, Z=0)\)

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QUESTION:

For the Transaction Processing Performance Council’s benchmark in Exercise 5-10, let X, Y , and Z denote the average number of selects, updates, and inserts operations required for each type of transaction, respectively. Calculate the following:

(a) \(f_{x y z}(x, y, z)\)

(b) Conditional probability mass function for X and Y given Z = 0

(c) \(P(X<6, Y<6 \mid Z=0)\)

(d) \(E(X \mid Y=0, Z=0)\)

ANSWER:

Step 1 of 4

A.

 The possible X values are given in the third column of the table, the possible Y values are given in the fourth column and the possible Z values are given in the fifth column.

The number of favorable outcomes for each category is the frequency (second column in the table).

The probability is the number of favorable outcomes divided by the number of possible outcomes:

\(\begin{array}{c}f_{XYZ}(23.0,\ 11,\ 12)=\frac{43}{100}=0.43\\ f_{XYZ}(4.2,\ 3,\ 1)=\frac{44}{100}=0.44\\ f_{XYZ}(11.4,\ 0,\ 0)=\frac{4}{100}=0.04\\ f_{XYZ}(130.0,\ 120,\ 0)=\frac{5}{100}=0.05\\ f_{XYZ}(0,\ 0,\ 0)=\frac{4}{100}=0.04\end{array}\)

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