Give the Probability Distribution for the Indicated Random Variable $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 6 } &\frac { 2 } { 3 } & \frac{ 1 } { 6 } \\\end{array}$

question 53

Multiple Choice

Give the probability distribution for the indicated random variable.
A fair coin is tossed three times, and we count the number of "runs" that occur. A "run" is defined as a sequence of one or more of the same letter (e.g., HTH is 3 runs, TTH is 2 runs, and TTT is 1 run) .

• A) \(\begin{array} { l }
• x & 1 & 2 & 3 \\
• P ( X = x ) &\frac { 1 } { 6 } &\frac { 2 } { 3 } & \frac{ 1 } { 6 } \\
• \end{array}\)
• B) \(\begin{array} { l }
• x & 1 & 2 & 3 \\
• P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } {3 } \\
• \end{array}\)
• C) \(\begin{array} { l }
• x & 1 & 2 & 3 \\
• P ( X = x ) &\frac { 1 } { 9 } &\frac { 7 } { 9 } & \frac{ 1 } { 9 } \\
• \end{array}\)
• D) \(\begin{array} { l }
• x & 1 & 2 & 3 \\
• P ( X = x ) &\frac { 1 } {8 } &\frac { 3 } { 4 } & \frac{ 1 } { 8 } \\
• \end{array}\)
• E) \(\begin{array} { l }
• x & 1 & 2 & 3 \\
• P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 2 } & \frac{ 1 } { 4 } \\
• \end{array}\)

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Definitions:

Labor Efficiency Variance

The difference between the budgeted and actual hours worked, multiplied by the standard labor rate, indicating efficiency in labor usage.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the expected (standard) variable overhead rate multiplied by the actual activity level.

June

The sixth month of the year in the Gregorian calendar, often associated with the start of summer in the northern hemisphere.

Materials Price Variance

A measure of the difference between the actual cost of materials and the standard cost, multiplied by the actual quantity of materials used.