Can a Probability Distribution Function Be Flat?

[reddvoid]

If probability distribution function is flat like a rectangular signal then probability density function which is differentiation of probability distribution function will have positive and negative impulses, but probability density function cannot be negative. . what's wrong in this . . . Can't probability distribution functio be flat ?

 

[mfb]

Sometimes, "probability distribution function" is used as "probability density function".

 

[Enthalpy]

The differentiated function is not a probability.

 

[rbj]

The differentiated function is not a probability.

neither is the rectangular function a distribution function. a distribution function must be an increasing function (so that the derivative, which is the p.d.f., is always non-negative).

 

[alphysicist]

There is nothing inherently wrong with a probability distribution function being flat. In fact, a flat PDF is often used to represent a uniform distribution. However, the issue with the statement is that the PDF cannot have positive and negative impulses. The PDF represents the likelihood of a random variable taking on a specific value, and it cannot have negative values. The statement may be confusing the PDF with the derivative of the PDF, which can have positive and negative values. However, the derivative is not the same as the PDF itself.