How is the cumulative distribution function (CDF) of the uniform distribution expressed?

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How is the cumulative distribution function (CDF) of the uniform distribution expressed?

The cumulative distribution function (CDF) of the uniform distribution is represented correctly by the equation F(x) = (x-a)/(b-a) for a uniform distribution defined on the interval [a, b]. This expression captures the proportion of values that fall below a certain value x within the specified range. In this context, 'a' is the minimum value of the distribution, and 'b' is the maximum value. The CDF is designed to output the probability that a randomly selected value from the distribution is less than or equal to x. As x approaches a from the left, F(x) approaches 0, reflecting that no values fall below the minimum point of the distribution. Conversely, when x reaches b, F(x) approaches 1, signifying that all values in the distribution are accounted for. The formulation (x-a)/(b-a) divides the distance from a to x by the total distance from a to b, effectively normalizing the range so that the CDF behaves appropriately within the interval [a, b]. It also ensures that the CDF is continuous and non-decreasing, fundamental characteristics of any cumulative distribution function. On the other hand, the other options do not properly reflect the cumulative probability for a uniform distribution

The cumulative distribution function (CDF) of the uniform distribution is represented correctly by the equation F(x) = (x-a)/(b-a) for a uniform distribution defined on the interval [a, b]. This expression captures the proportion of values that fall below a certain value x within the specified range.

In this context, 'a' is the minimum value of the distribution, and 'b' is the maximum value. The CDF is designed to output the probability that a randomly selected value from the distribution is less than or equal to x. As x approaches a from the left, F(x) approaches 0, reflecting that no values fall below the minimum point of the distribution. Conversely, when x reaches b, F(x) approaches 1, signifying that all values in the distribution are accounted for.

The formulation (x-a)/(b-a) divides the distance from a to x by the total distance from a to b, effectively normalizing the range so that the CDF behaves appropriately within the interval [a, b]. It also ensures that the CDF is continuous and non-decreasing, fundamental characteristics of any cumulative distribution function.

On the other hand, the other options do not properly reflect the cumulative probability for a uniform distribution

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