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Here is a rendered image along with a heat map of the sample counts to show this.  From left-to-right, the three teapots in this image have their relative pixel variance set to 20, 1, and 0, but are otherwise identical. The scene's pixel variance is intentionally set somewhat high to emphasize the difference in noise:

 

Before After Image Slider
methodoverlay
width730px
overlayedSlidertrue
leftImageimage_galleries_uuid_relPixVarImg.png-c3e5b85e-e5d9-43ca-b159-acb5f00f4319
rightImageimage_galleries_uuid_relpixvarsmp.png-6eded40f-4f4e-4bb4-8e77-94cd902dba61

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