The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is A. y – x B. $$\frac{1}{{{\text{y}} – {\text{x}}}}$$ C. x – y D. $$\frac{1}{{{\text{x}} – {\text{y}}}}$$

The correct answer is B. $\frac{1}{{{\text{y}} – {\text{x}}}}$.

A probability density function (PDF) is a function that describes the probability of a continuous random variable taking on a certain value. The PDF of a uniform distribution is a constant function over the interval of interest, and zero elsewhere. In this case, the interval of interest is $[x, y]$, so the PDF is $\frac{1}{{{\text{y}} – {\text{x}}}}$.

Option A, $y – x$, is not a probability density function because it is not non-negative and does not integrate to 1. Option C, $x – y$, is also not a probability density function because it is not non-negative. Option D, $\frac{1}{{{\text{x}} – {\text{y}}}}$, is not a probability density function because it is not defined for $x > y$.