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|See also: cumulative distribution, normal distribution,|
Next, our physicist wants to know how what the chances are of finding
more than 30 plums in the slice of the plum cake. One of the fundamental
properties of distribution diagrams is that the relative area between two
values on the x-axis reflect the chances that the corresponding event will
occur. In our example the physicist may draw a vertical line at 30 plums.
The relative area above this mark indicates the chance of finding more
than 30 plums in the slice of cake (which is roughly 10 %, according to
the distribution curve shown below).
Sometimes it may be inconvenient to determine the relative area. This complication can be avoided by scaling the distribution curve such that it has an area of exactly 1.0. When doing so, any area below the curve reflects the chances that an event may fall into that area. This curve is called the probability density function (pdf):
Hint: Do not confuse the scaling of the area with the scaling of the y-axis. A distribution curve scaled to an area of 1.0 does not have a maximum of 1.0; see also the for further explanation
Last Update: 2004-Jul-03