Introduction
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: 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: in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%.
If the random variable is real-valued (or more generally, if a total order is defined for its possible values), the cumulative distribution function gives the probability that the random variable is no larger than a given value; in the real-valued case it is the integral of the density.
Read more about this topic: Probability Distribution
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