Why divide histogram count by bin width in the PDF definition

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member 428835
hey pf!

can someone help me understand why a pdf is defined in the following manner: [tex]\lim_{\substack{N\to \infty\\ \Delta c \to 0}}\frac{H(c,\Delta c,N)}{\Delta c}[/tex] where [itex]\Delta c[/itex] is the width, [itex]N[/itex] is the observation number? Specifically, why the divisor? why is this necessary? [itex]H[/itex] is a histogram.

any insight is greatly appreciated!

thanks!
 
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I'm not familiar with your notation. However, in general, the integral of a pdf must be 1, so I presume the division is to insure that this holds.
 
sorry, i was worried about being too vague, but i think youre right.