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6.2 Normal Distribution:

The normal distribution was first discovered in 1733 by English mathematician De-Moivre, who obtained this continuous distribution as a limiting case of the binomial distribution and applied it to problems arising in the game of chance. It was also known to Laplace, no later than 1774 but through a historical error it was credited to Gauss, who first made in Astronomy. Gauss used the normal curve to describe the theory of accidental errors of measurements involved in the calculation of orbits of heavenly bodies. Throughout the eighteenth and nineteenth centuries, various efforts were made to establish the normal model as the underlying law ruling all continuous random variables. Thus, the name “normal”. These effors, however, failed because of false premises. The normal model has, nevertheless, become the most important probability model in statistical analysis.

A random variable X is said to have a normal distribution with parameters μ and σ2 if its density function is given by the probability law:

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