A Fair Die Is Rolled B) C) D) E)

question 141

Multiple Choice

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.

• A) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \\
• \end{array}\)
• B) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \\
• \end{array}\)
• C) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \\
• \end{array}\)
• D) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \\
• \end{array}\)
• E) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \\
• \end{array}\)

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Definitions:

Cost Of Goods Sold

The direct costs attributable to the production of goods sold by a company, including materials and labor.

Activity-Based Costing

A costing method that assigns costs to products or services based on the activities they require and the resources consumed by these activities.

Manufacturing Overhead Costs

Indirect costs associated with manufacturing, including costs related to running the factory that cannot be directly traced to specific units produced.

Expected Activity

Anticipated level of operations or production, based on forecasts or trends, which can influence budgeting and planning processes.