# Normal (Gaussian) distribution

• The normal distribution is defined by first two moments, mean (Âµ) and variance (Ïƒ2)
• The probability density function P(x) of normally distributed variable is given by:
• The probability of the value lying between a and b is given by:
• The expected value of a normally distributed variable: E[X]= Âµ,
• The variance of normally distributed variable: Var(X)= Ïƒ2
• If two variables are individually normally distributed, then the linear combination of the both is also normally distributed
• Lets take an example of two variable X1 and X2 which are normally distributed such that:
•  X1~N(Âµ1, Ïƒ1) and X2~N(Âµ2, Ïƒ2)
• Then X= a.X1+ b.X2 is also normally distributed

The skewness of normal distribution is = 0 and the kurtosis is = 3