Can a Probability Distribution Function Be Flat?

In summary, a probability density function (PDF) is a function used to describe the likelihood of a random variable taking on a specific value and represents the probability distribution of a continuous random variable. It differs from a probability distribution function (PDF) in that a PDF describes a continuous random variable while a PDF describes a discrete random variable. The area under a PDF curve represents the probability of an event occurring and is always equal to 1. PDFs are commonly used in statistics to calculate probabilities and compare distributions of different variables. A PDF cannot have negative values since it represents the probability of an event occurring.
  • #1
reddvoid
119
1
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 ?
 
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  • #2
Sometimes, "probability distribution function" is used as "probability density function".
 
  • #3
The differentiated function is not a probability.
 
  • #4
Enthalpy said:
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).
 
  • #5


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.
 

1. What is a probability density function (PDF)?

A probability density function (PDF) is a mathematical function that describes the likelihood of a random variable taking on a particular value. It is used to represent the probability distribution of a continuous random variable.

2. How is a PDF different from a probability distribution function (PDF)?

A PDF is a function that describes the probability distribution of a continuous random variable, while a probability distribution function (PDF) describes the probability distribution of a discrete random variable. A PDF is continuous, while a PDF is a series of discrete points.

3. What is the area under a PDF curve?

The area under a PDF curve represents the probability of an event occurring. The total area under the curve is equal to 1, which means that the probability of the event occurring is 100%.

4. How is a PDF used in statistics?

PDFs are used in statistics to describe the probability distribution of a continuous random variable. They are often used to calculate the probability of an event occurring within a certain range of values, or to compare the distribution of different variables.

5. Can a PDF be negative?

No, since a PDF represents the probability of an event occurring, it cannot have negative values. The area under the curve must always be positive, and therefore a PDF cannot be negative.

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