Physically Based Rendering by Matt Pharr

Author:Matt Pharr [Matt Pharr, Greg Humphreys]
Language: eng
Format: epub
ISBN: 978-0-123-78580-0
Publisher: Elsevier Science
Published: 2010-09-14T16:00:00+00:00

The expected value and variance have three important properties that follow immediately from their respective definitions:

These properties, and some simple algebraic manipulation, yield a much simpler expression for the variance:

Thus, the variance is the expected value of the square minus the square of the expected value. Given random variables that are independent, variance also has the property that the sum of the variances is equal to the variance of their sum:

13.2 THE MONTE CARLO ESTIMATOR

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