Give the Probability Distribution for the Indicated Random Variable A) $\begin{array} { l } x & 0 & 3& 6 \\P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 } \\\end{array}$

question 55

Multiple Choice

Give the probability distribution for the indicated random variable.
A black and white die are rolled, and consider the following random variable.
$X = \left\{ \begin{array} { l } 0 , \text { if both numbers are odd } \\3 , \text { if one number is odd and one is even } \\6 , \text { if both numbers are even }\end{array} \right.$

• A) \(\begin{array} { l }
• x & 0 & 3& 6 \\
• P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 } \\
• \end{array}\)
• B) \(\begin{array} { l }
• x & 0 & 3& 6 \\
• P ( X = x ) &\frac { 2 } { 3} &\frac { 1 } { 6 } & \frac{ 1 } { 6 } \\
• \end{array}\)
• C) \(\begin{array} { l }
• x & 0 & 3& 6 \\
• P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } \\
• \end{array}\)
• D) \(\begin{array} { l }
• x & 0 & 3& 6 \\
• P ( X = x ) &\frac { 1 } { 2 } &\frac { 1 } { 4 } & \frac{ 1 } { 4 } \\
• \end{array}\)
• E) \(\begin{array} { l }
• x & 0 & 3& 6 \\
• P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } {2 } & \frac{ 1 } { 4 } \\
• \end{array}\)

---

Definitions:

Positive Stimulus

An event or object that encourages a favorable response from an individual or system.

Unpleasant Stimulus

A negative or aversive event, object, or situation that can trigger or be used in behavioral responses, including avoidance or behavioral modification techniques.

Good Job

A commendation for performance that meets or exceeds expectations, often implying satisfaction with the work done.

Fixed-Ratio

A schedule of reinforcement where a response is rewarded only after a specified number of responses, leading to a high and steady rate of response.