Probability distribution Facts for Kids

The normal distribution, often called the "bell curve"

Probability distribution is a term from mathematics. Suppose there are many events with random outcomes. A probability distribution is the theoretical counterpart to the frequency distribution. A frequency distribution simply shows how many times a certain event occurred. A probability distribution says how many times it should have occurred in the long run (that is, its probability). The probability distribution of a random variable $X$ is often written as $f_X(x)$ (or simply $f(x)$ ). Such a distribution can either be discrete, taking a discrete (or countable) amount of values, or continuous, taking an uncountable amount of values (as from a continuous interval).

As an example, the probability distribution for a single roll of a normal 6-sided dice can be presented by:

Probability distribution for a dice roll event
Result	$1$	$2$	$3$	$4$	$5$	$6$
Probability of result	$\frac {1}{6}$	$\frac {1}{6}$	$\frac {1}{6}$	$\frac {1}{6}$	$\frac {1}{6}$	$\frac {1}{6}$

where result is the outcome of the dice roll, and the probability shows the chances of that result occurring. If we roll a dice 60 times, then in the long run, we should expect to have each side appear 10 times on average.

There are different probability distributions. Each of them has its use, its benefits and its drawbacks. Some common probability distributions include:

Probability density function

Images for kids

The left shows the probability density function. The right shows the cumulative distribution function, for which the value at a equals the area under the probability density curve to the left of a.
One solution for the Rabinovich–Fabrikant equations. What is the probability of observing a state on a certain place of the support (i.e., the red subset)?

Probability distribution facts for kids

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Images for kids

See also