To understand the difference between PDF and PMF, it is essential to understand what Random variables are. A random variable is a variable whose value is not known to the task; in other words, the value depends on the result of the experiment.
For instance, while flipping a coin, the value, i.e. heads or tails, depends upon the outcome.
PDF, also known as the probability density function, is a mathematical function that is used when there is a solution to be found within a range of continuous random variables. PMF, also known as probability mass function is a function that used discrete random variables to find a solution.
PDF and PMF are related to physics, statistics, calculus, or higher math. PDF (Probability Density Function) is the likelihood of the random variable in the range of discrete values.
On the other hand, PMF (Probability Mass Function) is the likelihood of the random variable in the range of continuous values.
| Parameter of Comparison | PMF | |
|---|---|---|
| Full form | Probability Density Function | Probability Mass Function |
| Use | PDF is used when there is a need to find a solution in a range of continuous random variables. | PMF is used when finding a solution in a range of discrete random variables is needed. |
| Random Variables | PDF uses continuous random variables. | PMF uses discrete random variables. |
| Formula | F(x)= P(a < x 0 | p(x)= P(X=x) |
| Solution | The solution falls in the radius range of continuous random variables | The Solutions fall in the radius between numbers of discrete random variables |
The Probability Density Function (PDF) depicts probability functions in terms of continuous random variable values between a precise range of values.
Also Read: Whistleblower vs Leaker: Difference and ComparisonIt is also known as a probability distribution function or a probability function. It is denoted by f(x).
The PDF is essentially a variable density over a given range. It is positive/non-negative at any given point in the graph, and the full PDF always equals one.
In a case where the probability of X on some given value x (continuous random variable) is always 0. P(X = x) does not work in such a case.
In such a situation, we need to calculate the probability of X resting in an interval (a, b) along with P(a< X< b) which can take place using a PDF.
The Probability distribution function formula is defined as, F(x)= P(a < x < b)= ∫ b a f(x)dx>0
Some instances where the Probability distribution function can work are:
Various applications of the probability density function (PDF) are:
The Probability Mass function depends on the values of any real number. It does not go to the value of X, which equals zero; in the case of x, the value of PMF is positive.
The PMF plays an important role in defining a discrete probability distribution and produces distinct outcomes. The formula of PMF is p(x)= P(X=x) i.e the probability of (x)= the probability (X=one specific x)
Also Read: ICSE vs IGCSE: Difference and ComparisonAs it gives distinct values, PMF is very useful in computer programming and the shaping of statistics.
In simpler terms, probability mass function or PMS is a function that is associated with discrete events, i.e. probabilities related to those events occurring.
The word “mass“ explains the probabilities focused on discrete events.
Some of the applications of the probability mass function (PMF) are:
Some instances where the Probability mass function can work are:
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