What is Density function: Definition and 191 Discussions

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would equal one sample compared to the other sample.
In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to 1.
The terms "probability distribution function" and "probability function" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables.

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  1. chwala

    Solve this problem that involves a probability density function

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  2. chwala

    Solve the problem involving probability density function

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  3. J

    Using Gauss's Law to Calculate Charge Density Function

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  4. chwala

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  5. A

    A Solving an Integral involving a probability density function

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  6. A

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  8. PainterGuy

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  9. N

    A Probability Density Function: Converting Experimental Observations to PDF

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  10. A

    A The name of this probability density function

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  11. P

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  12. M

    Finding marginal distribution of 2d of probability density function

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  13. A

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  14. A

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  15. A

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  16. A

    On the width of the kinetic energy distribution of a gas

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  17. megf

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  18. Vicol

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  19. shahbaznihal

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  20. Robin04

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  21. S

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  22. CivilSigma

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  23. Another

    I Please help explain the probability density function

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  24. S

    MHB Given probability density function find its cumulative distribution function

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  25. S

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  26. B

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  28. P

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  30. M

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  31. T

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  32. M

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  33. T

    I What Does The Probability Density Function Tell You?

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  34. Saracen Rue

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  35. Saracen Rue

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  37. NatFex

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  38. G

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  39. Schwarzschild90

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  40. Jan Wo

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  41. T

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  42. X

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  43. S

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  44. diracdelta

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  45. Lewis7879

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  46. D

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  47. Calpalned

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  48. C

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  49. Mr Davis 97

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  50. W

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