The importance of the probability distribution is as previously emphasized, but the normal distribution is considered to be the most important distribution.
As you increase the distribution of the points you observe, a normal curve is drawn when the expected value and variance approach the following values.
E(X) → \mu \\
V(X) → \sigma^2
A distribution that uses this normal curve as a density function is called a ** normal distribution **.
The common representation of the normal distribution N (μ, σ ^ 2) is that the expected value is μ and the variance is σ ^ 2 (the square of the standard deviation).
As mentioned above, the normal distribution is the distribution that can be said to assume it most often.
First of all, there are a large number of natural and social phenomena that are thought to follow a normal distribution.
Also, I explained in the asymptotic theory, but when dealing with large numbers, the distribution is as close as possible to the normal distribution. If you have forgotten, let's remember the Central Limit Theorem again.
When the population follows a normal distribution, the sample function has a well-known major distribution.
As I introduced earlier, the normal distribution N (0,1) with mean 0 variance 1 is called the standard normal distribution, and its mathematical table is called the normal distribution table. You can find any number of normal distribution tables by searching, but I always refer to the table below.
Standard normal distribution table http://www.koka.ac.jp/morigiwa/sjs/standard_normal_distribution.htm
Standard normal distribution table https://staff.aist.go.jp/t.ihara/normsdist.html
The equation of the normal curve (= probability density function of the normal distribution) can be written as follows.
y = \frac {1} {\sqrt{2\pi}\sigma}e^{-\frac {(x-\mu)^2} {2\sigma^2} }
Derivation of Z according to N (0,1) from this equation is called standardization.
X follows N (μ, σ ^ 2), and Z follows N (0,1).
This has also appeared so far, but I will introduce it again.
from scipy.stats import norm
print( norm.mean(), norm.std(), norm.var() )
#=> (0.0, 1.0, 1.0)
#The mean of the normal distribution is 0, and the standard deviation and variance are 1.
#Randomly generate 10 variables that follow a normal distribution
r = norm.rvs(size=10)
print( r )
# => [-0.14257586 1.4193167 -1.74553227 -0.1446086 -0.84588791 0.6521945 0.38792576 1.12649729 -1.04827952 1.26594555]
#Since it is random, a value close to the mean 0 variance 1 is observed.
print( r.mean(), r.std(), r.var() )
# => (0.092499564763084963, 1.0138488700256538, 1.0278895312522951)
Statistics (scipy.stats) http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html
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