Statistical Methods

Unit 2 - Probability distributions

2.7.The Normal Distribution
The normal distribution is one of the most important distributions in statistics; its equation was first given by De-Moivere in 1733. Later it was rediscovered and developed by Gauss in 1809 and by Laplace in 1812. Therefore, this distribution is sometimes referred to as Gaussian and Laplace distribution. The probability density function of a random variable having normal distribution is given by,

Where µ and are respectively the mean and standard deviation of the distribution. π and e are constant whose values are equal to 3.1416 and 2.7183 respectively. The graph of f(x) is a famous “bell-shaped” curve.

Normal distribution can be completely identified if mean (µ) and standard deviation () are known. The distribution will vary depending upon the values of m and S which are given in Fig (a) and Fig (b). It is a continuous distribution and can theoretically assume any value from - to +. However, for all practical purposes the values lie in the range of plus or minus three standard deviations from the mean.

Fig. a: Distributions with the same standard deviation but different means

Fig. b: Distribution with the same mean but different standard deviations