White Noise: The mathematical proof of zero correlation (in 2.5 min) #maths #discrete #mathematics

Ever wondered why white noise has zero memory and is completely uncorrelated over time? In this high-speed mathematical derivation, we unpack the autocovariance function and autocorrelation function (ACF) of a white noise process step-by-step, including a beautiful visual plot of the ACF.

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0:00 - Introduction to White Noise
0:10 - First Two Statistical Moments
0:20 - Independence Across Time
0:30 - Definition of Autocovariance
0:40 - Simplifying with Zero Mean
0:50 - Case 1: Autocovariance at Lag zero
1:00 - Evaluating gamma(0)
1:10 - Case 2: Autocovariance at Lag k != 0
1:20 - Expectation of Product
1:30 - Evaluating gamma(k) for k != 0
1:40 - Summary of Autocovariance Function
1:50 - Autocorrelation Function Definition
2:00 - Deriving the ACF (rho(k))
2:10 - Sketching the ACF Graph
2:20 - Why White Noise Observations are Uncorrelated

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Видео White Noise: The mathematical proof of zero correlation (in 2.5 min) #maths #discrete #mathematics канала nicefa