Saturday, September 10, 2022

Mean and Expected Value

The mean and expected values are closely related but there is a difference.

For example, we have 5 coins with 2 coins of five cents and 3 coins of 10 cents respectively. In this case, we calculate the mean by averaging the coin's values as Cmean = (1/5)*(5+5+10+10+10) = 8. Here, 8 is the Mean and not the expected value as the system state (coin's value) is not hidden.

Now, we have five different weight measures of the same person as: 79.8kg, 80kg, 80.1kg, 79.8kg, and 80.2kg. Here, the person is a system and the person's weight is the system's state. The measurements are different due to random errors in the weight scales and therefore the persons weight is a hidden state. We do not know the exact value of the person's weight but can make an estimate by averaging the scale's measurements as Wavg = (1/5)*(79.8 + 80 + 80.1 + 79.8 + 80.2) = 79.98kg. The outcome of this estimate is called the Expected Value.

(Source: https://www.kalmanfilter.net/background.html)

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