Question

For a continuous random variable, the total area beneath the PDF will be greater than zero but less than one. true or false

Answer 1

True.

Explanation:

The total area beneath the probability density function (PDF) of a continuous random variable must be greater than or equal to zero, because the probability of any specific outcome is always non-negative. However, the total area beneath the PDF may be less than or equal to one. In fact, it is only equal to one if the PDF is a valid density function.

For example, the PDF of a normal distribution has a total area beneath it of exactly one. However, the PDF of a uniform distribution has a total area beneath it of less than one, because the function has a constant value over a finite interval.