Posts filled under #t4tino23

Anche se secondo te fa ca

Anche se secondo te fa cagare la foto, la metto lo stesso perch voglio dirti che ti voglio bene, hai dimostrato anche oggi che persona gentile sei e che mi mancava quando mi prendevi in braccio per farmi diventare pi alta AHAHHAHAHA ci vediamo domani Volevo anche ringraziare tutte le persone che mi hanno fermato per una foto, abbracci e tutto il resto...non mi aspettavo tutte queste persone, non ora che ho "messo da parte" YouTube, davvero...siete stati tutti molto carini, sappiate che vi adoro e che adoro i vostri abbracci come nessun'altro, perch so che i vostri sono sinceri!! Ci vediamo domani per chi ci sar, taggatemi in tutte le foto! #mag #youtube #t4tino23 #vgs #vivalefiere

Ciao bello @T4tino23 e st

Ciao bello @T4tino23 e stato un piacere incontrarti ritornando foto vecchie nel tel . Un pokemon selvatico che spunta dietro haha #pokemongo #t4tino23 ----------------------------------------------------------------------------------- Se volete iscrivervi nel mio canale basta schiacciare il link della Bio del mio profilo instagram o scrivere su YouTube questo nikname (Gianluxtube) buona serata #YouTube#follow

Tatino mi ha messo mi pia

Tatino mi ha messo mi piace sul mio commento grande. TATINO REGNA #t4tino23#forever#

An extract on #t4tino23

The moment generating function of a real random variable X {\displaystyle X} is the expected value of e t X {\displaystyle e^{tX}} , as a function of the real parameter t {\displaystyle t} . For a normal distribution with density f {\displaystyle f} , mean {\displaystyle \mu } and deviation {\displaystyle \sigma } , the moment generating function exists and is equal to M ( t ) = E [ e t X ] = f ^ ( i t ) = e t e 1 2 2 t 2 {\displaystyle M(t)=\operatorname {E} [e^{tX}]={\hat {f}}(-it)=e^{\mu t}e^{{\tfrac {1}{2}}\sigma ^{2}t^{2}}} The cumulant generating function is the logarithm of the moment generating function, namely g ( t ) = ln M ( t ) = t + 1 2 2 t 2 {\displaystyle g(t)=\ln M(t)=\mu t+{\tfrac {1}{2}}\sigma ^{2}t^{2}} Since this is a quadratic polynomial in t {\displaystyle t} , only the first two cumulants are nonzero, namely the mean {\displaystyle \mu } and the variance 2 {\displaystyle \sigma ^{2}} .

If X is distributed normally with mean and variance 2, then The exponential of X is distributed log-normally: eX ~ ln(N (, 2)). The absolute value of X has folded normal distribution: |X| ~ Nf (, 2). If = 0 this is known as the half-normal distribution. The absolute value of normalized residuals, |X - |/, has chi distribution with one degree of freedom: |X - |/ ~ 1(|X - |/). The square of X/ has the noncentral chi-squared distribution with one degree of freedom: X2/2 ~ 21(2/2). If = 0, the distribution is called simply chi-squared. The distribution of the variable X restricted to an interval [a, b] is called the truncated normal distribution. (X )2 has a Lvy distribution with location 0 and scale 2.

By Cochran's theorem, for normal distributions the sample mean ^ {\displaystyle \scriptstyle {\hat {\mu }}} and the sample variance s2 are independent, which means there can be no gain in considering their joint distribution. There is also a converse theorem: if in a sample the sample mean and sample variance are independent, then the sample must have come from the normal distribution. The independence between ^ {\displaystyle \scriptstyle {\hat {\mu }}} and s can be employed to construct the so-called t-statistic: t = ^ s / n = x 1 n ( n 1 ) ( x i x ) 2 t n 1 {\displaystyle t={\frac {{\hat {\mu }}-\mu }{s/{\sqrt {n}}}}={\frac {{\overline {x}}-\mu }{\sqrt {{\frac {1}{n(n-1)}}\sum (x_{i}-{\overline {x}})^{2}}}}\ \sim \ t_{n-1}} This quantity t has the Student's t-distribution with (n 1) degrees of freedom, and it is an ancillary statistic (independent of the value of the parameters). Inverting the distribution of this t-statistics will allow us to construct the confidence interval for ; similarly, inverting the 2 distribution of the statistic s2 will give us the confidence interval for 2: [ ^ t n 1 , 1 / 2 1 n s , ^ + t n 1 , 1 / 2 1 n s ] [ ^ | z / 2 | 1 n s , ^ + | z / 2 | 1 n s ] , 2 [ ( n 1 ) s 2 n 1 , 1 / 2 2 , ( n 1 ) s 2 n 1 , / 2 2 ] [ s 2 | z / 2 | 2 n s 2 , s 2 + | z / 2 | 2 n s 2 ] , {\displaystyle {\begin{aligned}&\mu \in \left[\,{\hat {\mu }}-t_{n-1,1-\alpha /2}\,{\frac {1}{\sqrt {n}}}s,\ \ {\hat {\mu }}+t_{n-1,1-\alpha /2}\,{\frac {1}{\sqrt {n}}}s\,\right]\approx \left[\,{\hat {\mu }}-|z_{\alpha /2}|{\frac {1}{\sqrt {n}}}s,\ \ {\hat {\mu }}+|z_{\alpha /2}|{\frac {1}{\sqrt {n}}}s\,\right],\\&\sigma ^{2}\in \left[\,{\frac {(n-1)s^{2}}{\chi _{n-1,1-\alpha /2}^{2}}},\ \ {\frac {(n-1)s^{2}}{\chi _{n-1,\alpha /2}^{2}}}\,\right]\approx \left[\,s^{2}-|z_{\alpha /2}|{\frac {\sqrt {2}}{\sqrt {n}}}s^{2},\ \ s^{2}+|z_{\alpha /2}|{\frac {\sqrt {2}}{\sqrt {n}}}s^{2}\,\right],\end{aligned}}} where tk,p and 2k,p are the pth quantiles of the t- and 2-distributions respectively. These confidence intervals are of the confidence level 1 , meaning that the true values and 2 fall outside of these intervals with probability (or significance level) . In practice people usually take = 5%, resulting in the 95% confidence intervals. The approximate formulas in the display above were derived from the asymptotic distributions of ^ {\displaystyle \scriptstyle {\hat {\mu }}} and s2. The approximate formulas become valid for large values of n, and are more convenient for the manual calculation since the standard normal quantiles z/2 do not depend on n. In particular, the most popular value of = 5%, results in |z0.025| = 1.96.

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