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this paper and also wiki here, show CDF as follows (different letters, but same concept):

Given PDF $f_{X}$: $$P\{X\in \chi\} = \int_\chi{f_{X}(x) dx} $$

Then CDF $F_{X}(x)$ is defined as: $$ F_{X}(x)=\int_{-\infty}^{x} f_X (z) dz$$

My question is, where is the $z$ coming from? If you look at a plot of CDF, the $x$-axis still shows, well, $x$. Wiki has $t$ instead of $z$.

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1 Answer 1

up vote 3 down vote accepted

$z$ there is just a dummy variable. One can use anything other than $x$ there to avoid confusion since one takes the integral from $-\infty$ to $x$.

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