Probability Density Function (PDF)
In probability theory, a probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. The probability for the random variable to fall within a particular region is given by the integral of this variable’s density over the region. The probability density function is non-negative everywhere, and its integral over the entire space is equal to one.
A random variable X has (probability) density f, where f is a non-negative Lebesgue-integrable function. Hence, if F is the cumulative distribution function of X, f(x) = dF(x) / dx. Intuitively, one can think of f(x)dx as being the probability of X falling within the infinitesimal interval [x, x + dx]
Probability Mass Function (PMF)
In probability theory and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables, given that the distribution is discrete.
A probability mass function differs from a probability density function (p.d.f.) in that the latter is associated with continuous rather than discrete random variables; the values of the latter are not probabilities as such: a p.d.f. must be integrated over an interval to yield a probability.
Probability Distribution
To define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: for example, when throwing a die, each of the six values 1 to 6 has the probability 1/6. In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals.
References
- http://en.wikipedia.org/wiki/Probability_distribution
- http://en.wikipedia.org/wiki/Probability_density_function
- http://en.wikipedia.org/wiki/Probability_mass_function