Probability distribution: Difference between revisions

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However, for the same use case, it is possible to meet quality control requirements such as that a package of "500 g" of ham must weigh between 490 g and 510 g with at least 98% probability. This is possible because this measurement does not require as much precision from the underlying equipment.
 
[[File:Combined Cumulative Distribution Graphs.png|thumb|455x455px| Figure 1: The leftright graph shows a probability density function. The rightleft graph shows the cumulative distribution function, for which the value at {{font color|#ED1C24|'''a'''}} equals the area under the probability density curve to the left of {{font color|#ED1C24|'''a'''}}.]]
Absolutely continuous probability distributions can be described in several ways. The [[probability density function]] describes the [[infinitesimal]] probability of any given value, and the probability that the outcome lies in a given interval can be computed by [[Integration (mathematics)|integrating]] the probability density function over that interval.<ref name=":3"/> An alternative description of the distribution is by means of the [[cumulative distribution function]], which describes the probability that the random variable is no larger than a given value (i.e., <math>\ \boldsymbol\mathcal{P}(X < x)\ </math> for some {{nobr|<math>\ x\ </math>).}} The cumulative distribution function is the area under the [[probability density function]] from <math>\ -\infty\ </math> to <math>\ x\ ,</math> as shown in figure 1.<ref name='dekking'>{{cite book |last=Dekking |first=Michel (1946–) |year=2005 |title=A Modern Introduction to Probability and Statistics : Understanding why and how |publisher=Springer |isbn=978-1-85233-896-1 |___location=London, UK |oclc=262680588}}</ref>