Probability Density Function of Uniform Distribution

If we have a uniform distribution from A = 2 to B = 6, what is the value of the probability density function $f(X)$?

In the realm of continuous probability distributions, the uniform distribution is a fundamental concept where all outcomes in a specified range are equally likely. For a continuous uniform distribution defined from A to B, every point within the interval has an equal probability of occurring. This makes the calculation of the probability density function (PDF) straightforward because it is constant over the range. The key to solving such problems lies in understanding the nature of the uniform distribution, which simplifies the complexity inherent in other probability distributions by having a single, flat line as its PDF. This characteristic makes it an ideal starting point for students beginning to explore the world of continuous random variables.

In this particular problem, recognizing that the question pertains to a uniform distribution is crucial. The PDF of a uniform distribution is determined by the formula $\frac{1}{B - A}$. This helps in understanding that for any range [A,B], the density function will be a constant value that ensures the total area under the curve over that interval equals one, preserving the foundational probability principle. By focusing on the endpoints of the interval, students gain insight into the scaling factor that adjusts the height of the constant function to reflect the properties of probabilities. Moreover, this problem encourages considering how continuous distributions differ from discrete ones, especially in terms of how probabilities are distributed over an interval of infinite points rather than a set of discrete outcomes.