Function of distribution

In Probability, the function of distribution of a Random variable X is the function $\backslash \; F\_X$ which with any reality $x$ associates

$F\_X\; (X)\; =\; P\; X.$

The function of distribution of a continuous random variable is the Primitive of the Densité of probability $\backslash \; f\_X$.

$F\_X\; (X)\; =\; \backslash \; int\_\; \{-\; \backslash \; infty\}\; ^\; \{X\}\; f\_X\; (T)\; \backslash ,\; dt$

The function of distribution has the following properties:

• F_X is increasing.

• It is continuous everywhere on the right. and in any point $\backslash \; x\_0$ a limit, equal to .
• $\backslash \; lim\_\; \{X\; \backslash \; to\; -\; \backslash \; infty\}\; F\_X\; (X)\; =\; 0$
• $\backslash \; lim\_\; \{X\; \backslash \; to\; +\; \backslash \; infty\}\; F\_X\; (X)\; =1$

---- principal Article: Random variable

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