Normal Distribution

The normal (or Gaussian) distribution is a continuous probability distribution that is commonly used to model real-world data. It is defined by its mean (μ) and standard deviation (σ), and it has a bell-shaped curve that is symmetrical around the mean.

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The normal distribution has several important properties:

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1. Mean, median, and mode: The mean, median, and mode of a normal distribution are equal and equal to the mean (μ).

2. Symmetry: The normal distribution is symmetrical around the mean, meaning that the left and right tails of the distribution are mirror images of each other.

3. Area under the curve: The area under the curve of the normal distribution is equal to 1, meaning that the total probability of all possible outcomes is equal to 1.

4. Standard normal distribution: A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

 

In Python, the normal distribution can be generated using the numpy library. For example, the following code generates random numbers from a normal distribution with mean 0 and standard deviation 1.

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This normal distribution can be visualized using a histogram and a probability density function (PDF):

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import matplotlib.pyplot as plt
import seaborn as sns

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sns.distplot(data, kde=True, hist=True, norm_hist=True)
 

plt.show()

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The normal distribution is widely used in many areas, including finance, engineering, and medicine, to model the distribution of various variables. However, it is important to note that the normality assumption is often not met in real-world data, and it is necessary to check the normality of the data before applying statistical methods that assume normality.