To make training the network easier, we standardize each of the continuous variables. That is, we'll shift and scale the variables such that they have zero mean and a standard deviation of 1.

The scaling factors are

**saved**so we can go backwards when we use the network for predictions.

**SHIFTING**

If we have one random variable, that is constructed by adding a constant to another random variable

- We would shift the
**mean**by that constant - It would not shift the
**standard deviation**

**SCALING**

If we try to scale a random variable by multiplying a constant then we get a random variable

- It would effect both
**standard deviation**and**mean**

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Scaling and shifting are fundamental operations performed on random variables that significantly impact their behavior and the information they convey. Here's a breakdown of their individual effects:

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Scaling a Random Variable:

Multiplying by a constant (k): When you multiply a random variable X by a constant k, it affects both the mean (average) and standard deviation:

Mean: The new mean becomes k * μ (mu), where μ is the original mean of X.

If k is positive (e.g., multiplying by 2), the mean is scaled proportionally in the same direction.

If k is negative (e.g., multiplying by -2), the mean is scaled in the opposite direction and flips sign.

Standard Deviation: The standard deviation (σ) is also scaled by the absolute value of k: new standard deviation = |k| * σ.

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The standard deviation increases proportionally with the absolute value of k.

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