Normal Distribution

The probability density of normal distribution is:

• is the mean (or expectation) of the distribution. It is also equal to median and mode of the distribution.
• is the variance.
• is the standard deviation.
  
  

Standard Normal Distribution

If and , then the normal distribution is known as standard normal distribution:

Every normal distribution can be represented as standard normal distribution:

Cumulative Probability

Consider a real-valued random variable, . The cumulative distribution function of (or just the distribution function of ) evaluated at is the probability that will take a value less than or equal to :

The cumulative distribution function for a function with normal distribution is:

Where is the error function:

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