Which parameter defines the width of a uniform distribution?

Which parameter defines the width of a uniform distribution?

• A. λ
• B. Interval [a,b]
• C. Mean
• D. Variance

Answer: (B)

The width of a uniform distribution is determined by the interval [a, b], which represents the range of values that the random variable can take. In a uniform distribution, every value within this interval is equally likely to occur, and the length of the interval, given by b - a, directly affects the probability assigned to each value. The uniform distribution can be represented as U(a, b), where 'a' is the minimum value and 'b' is the maximum value. The parameters for this distribution indicate that any value between 'a' and 'b' has the same probability density, effectively creating a rectangular shape on a graph where the base is determined by the width of the interval. The correct choice focuses on how the definition of the interval directly links to the distribution's characteristics, including the overall spread and probability distribution, underscoring the importance of the interval in defining the uniform distribution's shape.

The width of a uniform distribution is determined by the interval [a, b], which represents the range of values that the random variable can take. In a uniform distribution, every value within this interval is equally likely to occur, and the length of the interval, given by b - a, directly affects the probability assigned to each value.

The uniform distribution can be represented as U(a, b), where 'a' is the minimum value and 'b' is the maximum value. The parameters for this distribution indicate that any value between 'a' and 'b' has the same probability density, effectively creating a rectangular shape on a graph where the base is determined by the width of the interval.

The correct choice focuses on how the definition of the interval directly links to the distribution's characteristics, including the overall spread and probability distribution, underscoring the importance of the interval in defining the uniform distribution's shape.