What is the probability density function (PDF) of the uniform distribution defined as?

What is the probability density function (PDF) of the uniform distribution defined as?

• A. f(x) = e^(x-a)
• B. f(x) = 1/(b-a)
• C. f(x) = (b-a)x
• D. f(x) = (b-a)/(x-a)

Answer: (B)

The probability density function (PDF) of a uniform distribution is defined in a very specific way. For a continuous uniform distribution defined on the interval [a, b], the PDF is constant within that interval and zero outside of it. The formula for the PDF is given by: f(x) = 1 / (b - a) for x in [a, b]. This means that the height of the density function is equal to the reciprocal of the length of the interval (b - a), ensuring that the total area under the PDF over the interval [a, b] sums to 1, which is a fundamental property of probability distributions. Since the uniform distribution assigns equal probability to all outcomes within the interval, the resulting function is flat, confirming that the correct answer outlines this characteristic accurately. The formula reflects the uniform distribution's principles, representing the equal likelihood of all values in the given range.

The probability density function (PDF) of a uniform distribution is defined in a very specific way. For a continuous uniform distribution defined on the interval [a, b], the PDF is constant within that interval and zero outside of it. The formula for the PDF is given by:

f(x) = 1 / (b - a) for x in [a, b].

This means that the height of the density function is equal to the reciprocal of the length of the interval (b - a), ensuring that the total area under the PDF over the interval [a, b] sums to 1, which is a fundamental property of probability distributions.

Since the uniform distribution assigns equal probability to all outcomes within the interval, the resulting function is flat, confirming that the correct answer outlines this characteristic accurately. The formula reflects the uniform distribution's principles, representing the equal likelihood of all values in the given range.