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:

Conditioned Stimulus

A previously neutral stimulus that, after association with an unconditioned stimulus, elicits a conditioned response.

Classical Conditioning

A training mechanism in which two stimuli are frequently paired together; over time, the response that was originally caused by the second stimulus is elicited by the first stimulus.

Unconditioned Response

A reflexive, instinctual reaction to an unconditioned stimulus, not learned through previous experience.

Conditioned Response

A learned reaction to a conditioned stimulus that occurs because of previous conditioning, an essential concept in classical conditioning theories.