Question

Probability distribution function vs probability density function

Answer 1

The probability distribution function / probability function has ambiguous definition. They may be referred to:
Probability density function (PDF)
Cumulative distribution function (CDF)
Or probability mass function (PMF) (statement from Wikipedia)
But what confirm is:
Discrete case: Probability Mass Function (PMF)
Continuous case: Probability Density Function (PDF)
Both cases: Cumulative distribution function (CDF)
Probability at certain x value, P(X = x) can be directly obtained in:
PMF for discrete case
PDF for continuous case
Probability for values less than x, P(X < x) or Probability for values within a range from a to b, P(a < X < b) can be directly obtained in:
CDF for both discrete / continuous case
Distribution function is referred to CDF or Cumulative Frequency Function (more commonly)

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