View source for University of Alberta Guide:STAT:222:Formulas and Functions:Cumulative Distribution Functions

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The <math>F_{X}(x) \rightarrow (cdf)\,</math>, represents the probability that the value of a random variable <math>X\,</math>, regardless of its distribution, will be less than or equal to the value <math>x\,</math> that is provided.  For continuous random variables, <math>F_{X}(0) = 0\,</math> because <math>P(X = 0) = 0\,</math> for all continuous random variables.  Therefore, all cumulative distribution functions will start at zero.
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Generally, <math>F_{X}(x)\,</math> represents <math>P(X \leq x)\,</math>, however, if what is desired is <math>P(X > x)\,</math> then <math>1 - F_{X}(x)\,</math> would be used.
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'''CDF for an Exponential RV'''<br>
[[Image:Exponential distribution cdf.png|325px|Cumulative distribution function]]
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Notice that as <math>x\,</math> increases, the probability nears closer and closer to one.  This is because as <math>x\,</math> increases, the area under the curve of the PDF becomes closer and closer to one.

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