Calculation of measurement errors.

Let n is count of measurements then the standard deviation is
\begin{equation}
\sigma = \sqrt{\frac{1}{n(n-1)}\sum\limits_{i=1}^{n}(\Delta x_{i})^2 },
\end{equation}
where \(\Delta x_{i}=x_{i}-\overline{x}\), \(\overline{x}\) is the sample mean. The confidence interval is \(\Delta_{\sigma}x = t_{n,\alpha}\sigma\), where \(t_{n,\alpha}\) is a Student’s t distribution with n − 1 degrees of freedom, \(\alpha=0.95\) (the 95th percentile). We use the function stats.t.ppf((1.0 + 0.95)/2, n-1) from the ‘stats’ package.
Then \(x = \overline{x} \pm \Delta_{s}x\).

In other denotes, the standard deviation is

\(\sigma = \sqrt{\operatorname {Var}(x_{ar}) / (n-1)}\),
where \(\operatorname {Var}(x_{ar})\) is variance and n is count of measurements.
The confidence interval is
\(\Delta_{\sigma}x = \sigma\overline{x}/\sqrt{n}\) (for examle, see wiki

Where X is the sample mean, and S2 is the sample variance. Then has a Student’s t distribution with kn − 1 degrees of freedom Example: alfa = 0.95, from a student t = 3.18 for kn = 4; 0.95 - confidence interval , 60-1 degrees of freedom denoting ppf as the 95th percentile of this distribution We usage function stats.t.ppf((1 + 0.95)/2, kn-1) from scipy package (from scipy import stats)

==================== Formula

The mass-energy equivalence is described by the famous equation \(E=mc^2\) discovered in 1905 by Albert Einstein.
In natural units (\(c = 1\)), the formula expresses the identity

\begin{equation} E=m \end{equation} Subscripts in math mode are written as \(a_b\) and superscripts are written as \(a^b\). These can be combined an nested to write expressions such as

\begin{equation} T^{i_1 i_2 \dots i_p}{j_1 j_2 \dots j_q} = T(x^{i_1},\dots,x^{i_p},e_{j_1},\dots,e_{j_q}) \end{equation}

We write integrals using $\int$ and fractions using \(\frac{a}{b}\). Limits are placed on integrals using superscripts and subscripts: \begin{equation} \int_0^1 \frac{dx}{e^x} = \frac{e-1}{e} \end{equation} Lower case Greek letters are written as \(\omega\), \(\delta\) etc. while upper case Greek letters are written as \(\Omega\), \(\Delta\).

Mathematical operators are prefixed with a backslash as \(\sin(\beta), \cos(\alpha), \log(x)\) etc.

A quantum superposition of the “basis states”
\begin{equation} |\psi\rangle = c_1|0\rangle + c_2|1\rangle , \end{equation} here \(|0\rangle\) and \(|1\rangle\) are the Dirac notation for the quantum state that will always give the result 0 or 1 when make a measurement.

Figure 1: A general structure UML2 SP
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Figure 1: A general structure UML2 SP

Experiment result is depicted in table 2

№	\(AB\)	\(BC\)	\(AC\)	\(N[A^+,B^+] <\)	\(N[B^-,C^-]+N[A^+,C^+]\)
1	240°	60°	300°	15	11
2	240°	60°	300°	15	11

xperiment result is depicted in table

№	\(\mid m_1\rangle\)	\(\mid m_2\rangle\)	\(\mid l_1\rangle\)	\(\mid l_1\rangle\)
1	1.0	0.0	0.497	0.503
2	0.499	0.501	1.0	0.0