Normal Distribution
Main Concept

For any distribution , the mean, denoted , is the expected value of X. The variance , , is the expected value of the square of the difference between the value of the X and its mean. The square root of the variance, , is called the standard deviation. Both variance and standard deviation measure how much X varies.
A random variable X is normal or Gaussian if its probability density function is given by:
where is its mean and its standard deviation.
The normal distribution is considered the most prominent probability distribution in statistics. The graph of the probability density is known as the "bell curve".
The standard normal distribution has a mean = 0, and standard deviation .



Adjust the mean and to see how the bell curve changes. Sample a set of points from the distribution and see how closely the sample matches the curve.

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