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A random variable is said to follow a normal distribution with mean and variance if its density function is written in the form:

Properties:

Take
• values \u200b\u200baround.
• function is symmetric about .

• Strictly and strictly increasing if decreasing if .
• has a maximum.

• has turning points and .
• In has a horizontal asymptote.

Features:

1. Hope: Hope is distribution.
2. Variance: The variance of the distribution is .
3. moment generating function: The moment generating function is
   


origin and scale change: The variable is not affected by changes of origin and scale, ie if then has the following distribution