We can only "shoot bullets from the ground straight up"! We need the inverse function! The problem is that for this function, the y axis is the output and the x axis is the input. See how the density of the bullets on the ground correspond to our desired distribution! We're almost there! As the bullets hit the line, they drop down to the ground: To see how this is useful, imagine that we shoot bullets from left to right at uniformly distributed heights. Intuitively: While PDF( x) describes the number of random values at x, CDF( x) describes the number of random values less than x. The CDF is, as the name suggests, the cumulative version of the PDF.
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