The two words ''cumulative'' and ''density'' contradict each other. GivenThe value of a graphdensity function in an interval about a point depends only on probabities of thesets probabilityin densityarbitrarily functionsmall neighborhoods of that point, so it is not cumulative.
<math display="block"> y=f(x),</math>
<math>y</math> is the probability of finding just the particular value of the variable corresponding to <math>x</math> on the <math>x</math>-axis. It knows nothing about the probabilities to be found at other values of <math>x</math>, and therefore cannot be ''cumulative''. The cumulative distribution function, by contrast, is an accumulation of the probabilities of finding every value of <math>x</math> up to and including the current value indicated on the <math>x</math>-axis.
