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Can variance be zero in normal distribution?
With variance being zero, the PDF of a normal distribution can be considered as a Dirac delta distribution, which is zero everywhere except of the location of the mean, where its function value is infinite.
What is the mean and variance of for standard normal distribution?
A standard normal distribution is a normal distribution with zero mean ( ) and unit variance ( ), given by the probability density function and distribution function. (1) (2) over the domain .
How to generate zero mean and unit variance?
To generate zero mean and unit variance, you are looking at standardization. Where a feature x becomes scaled feature z like this: Where μ is the mean of that feature and σ the standard deviation. Thanks for contributing an answer to Data Science Stack Exchange!
What is the mean of a probability distribution?
There are two important statistics associated with any probability distribution, the mean of a distribution and the variance of a distribution. The mean is defined as the expected value of the random variable itself. The Greek letter μ is usually used to represent the mean.
Why is unit variance important in machine learning?
In case of unit variance, that is because lots of machine learning algorithms use some kind of distance (e.g. Euclidean) to decide or predict. If a particular feature has broad values (i.e. large variance), the distance will be highly affected by that feature and the effect of other features will be ignored.
The variance is defined as the expected value of ( u − μ) 2. The variance measures how dispersed the data are. If the variance is large, the data are—on average—farther from the mean than they are if the variance is small. The standard deviation is the square root of the variance. The Greek letter σ is usually used to denote the standard deviation.