Applets:Binomial and Poisson Distribution (Applet) - Revision history

Noah at 20:40, 26 March 2023

2023-03-26T20:40:48Z

Hwang at 12:19, 18 January 2023

2023-01-18T12:19:04Z

Javier: Text replacement - "”" to """

2021-05-28T14:48:47Z

Text replacement - "”" to """

Javier: Text replacement - "„" to """

2021-05-28T14:46:30Z

Text replacement - "„" to """

Guenter at 10:01, 27 January 2021

2021-01-27T10:01:29Z

Guenter at 10:56, 19 January 2021

2021-01-19T10:56:34Z

Guenter at 10:43, 19 January 2021

2021-01-19T10:43:31Z

Javier: Text replacement - "[[Biografien_und_Bibliografien" to "[[Biographies_and_Bibliographies"

2020-07-09T12:53:22Z

Text replacement - "[[Biografien_und_Bibliografien" to "[[Biographies_and_Bibliographies"

Tasnad at 20:45, 9 June 2020

2020-06-09T20:45:37Z

Jimmy: /* Applet Manual */

2018-03-12T04:27:14Z

Applet Manual

@@ Line 5: / Line 5: @@
 This applet allows the calculation and graphical display of
-*the probabilities ${\rm Pr}(z=\mu)$ of a discrete random variable $z \in \{\mu \} =  \{0, 1, 2, 3, \text{...} \}$, that determine its ''Probability Density Function'' (PDF) &ndash; here representation with Dirac functions ${\rm \delta}( z-\mu)$:
+*the probabilities ${\rm Pr}(z=\mu)$ of a discrete random variable $z \in \{\mu \} =  \{0, 1, 2, 3, \text{...} \}$, that determine its ''Probability Density Function'' (PDF) &ndash; here representation with Dirac delta functions ${\rm \delta}( z-\mu)$:
 :$$f_{z}(z)=\sum_{\mu=1}^{M}{\rm Pr}(z=\mu)\cdot {\rm \delta}( z-\mu),$$
 *the probabilities ${\rm Pr}(z \le \mu)$ of the ''Cumulative Distribution Function'' (CDF):
@@ Line 71: / Line 71: @@
-the new random variable $f$  ("Error per block") calculates to:
+the new random variable $f$  ("error per block") calculates to:
 :$$f=\sum_{i=1}^{I}e_i.$$
@@ Line 113: / Line 113: @@
 We can see that for the Poisson distribution $\sigma^2 = m_1 = \lambda$ always holds. In contrast, the moments of the Binomial distribution always fulfill $\sigma^2 < m_1$.
-[[File: P_ID616__Sto_T_2_4_S2neu.png |frame| Moments of Poisson Distribution | rechts]]
+[[File: P_ID616__Sto_T_2_4_S2neu.png |frame| Moments of Poisson Distribution]]
 {{GraueBox|TEXT=
 $\text{Example 2:}$&nbsp;

@@ Line 51: / Line 51: @@
 We can derive the formulas for
 *the linear average:  &nbsp; $m_1 = I\cdot p,$
-*the quadratic average: &nbsp; $m_2 = (I^2-I)\cdot p^2+I\cdot p,$
+*the second moment: &nbsp; $m_2 = (I^2-I)\cdot p^2+I\cdot p,$
 *the variance and standard deviation:  &nbsp; $\sigma^2 = {m_2 - m_1^2} = {I \cdot p\cdot (1-p)} \hspace{0.3cm}\Rightarrow \hspace{0.3cm}
 \sigma =  \sqrt{I \cdot p\cdot (1-p)}.$

@@ Line 71: / Line 71: @@
-the new random variable $f$  ("Error per block&rdquo;) calculates to:
+the new random variable $f$  ("Error per block") calculates to:
 :$$f=\sum_{i=1}^{I}e_i.$$
@@ Line 250: / Line 250: @@
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Variation possibilities for the graphic display
-$\hspace{1.5cm}$"$+$&rdquo; (Zoom in),
+$\hspace{1.5cm}$"$+$" (Zoom in),
-$\hspace{1.5cm}$ "$-$&rdquo; (Zoom out)
+$\hspace{1.5cm}$ "$-$" (Zoom out)
-$\hspace{1.5cm}$ "$\rm o$&rdquo; (Reset)
+$\hspace{1.5cm}$ "$\rm o$" (Reset)
-$\hspace{1.5cm}$ "$\leftarrow$&rdquo; (Move left),  etc.
+$\hspace{1.5cm}$ "$\leftarrow$" (Move left),  etc.
 &nbsp; &nbsp; '''( I )''' &nbsp; &nbsp; Output of ${\rm Pr} (z = \mu)$ and ${\rm Pr} (z  \le \mu)$
@@ Line 268: / Line 268: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the&nbsp;  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&nbsp; of the&nbsp; [https://www.tum.de/ Technische Universität München].
-*The original version was created in 2003 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using "FlashMX&ndash;Actionscript&rdquo;&nbsp;  (Supervisor:&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The original version was created in 2003 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using "FlashMX&ndash;Actionscript"&nbsp;  (Supervisor:&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
 *In 2018 this Applet was redesigned and updated to &quot;HTML5&quot; by&nbsp;  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]]&nbsp; as part of his Bachelor's thesis (Supervisor:&nbsp; [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .

@@ Line 71: / Line 71: @@
-the new random variable $f$  (&bdquo;Error per block&rdquo;) calculates to:
+the new random variable $f$  ("Error per block&rdquo;) calculates to:
 :$$f=\sum_{i=1}^{I}e_i.$$
@@ Line 250: / Line 250: @@
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Variation possibilities for the graphic display
-$\hspace{1.5cm}$&bdquo;$+$&rdquo; (Zoom in),
+$\hspace{1.5cm}$"$+$&rdquo; (Zoom in),
-$\hspace{1.5cm}$ &bdquo;$-$&rdquo; (Zoom out)
+$\hspace{1.5cm}$ "$-$&rdquo; (Zoom out)
-$\hspace{1.5cm}$ &bdquo;$\rm o$&rdquo; (Reset)
+$\hspace{1.5cm}$ "$\rm o$&rdquo; (Reset)
-$\hspace{1.5cm}$ &bdquo;$\leftarrow$&rdquo; (Move left),  etc.
+$\hspace{1.5cm}$ "$\leftarrow$&rdquo; (Move left),  etc.
 &nbsp; &nbsp; '''( I )''' &nbsp; &nbsp; Output of ${\rm Pr} (z = \mu)$ and ${\rm Pr} (z  \le \mu)$
@@ Line 268: / Line 268: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the&nbsp;  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&nbsp; of the&nbsp; [https://www.tum.de/ Technische Universität München].
-*The original version was created in 2003 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using &bdquo;FlashMX&ndash;Actionscript&rdquo;&nbsp;  (Supervisor:&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The original version was created in 2003 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using "FlashMX&ndash;Actionscript&rdquo;&nbsp;  (Supervisor:&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
 *In 2018 this Applet was redesigned and updated to &quot;HTML5&quot; by&nbsp;  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]]&nbsp; as part of his Bachelor's thesis (Supervisor:&nbsp; [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .

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-{{LntAppletLinkEn|binomPoissonDistributions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Binomial-_und_Poissonverteilung_(Applet) '''German Version''']
+{{LntAppletLinkEn|binomPoissonDistributions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Binomial-_und_Poissonverteilung_(Applet) '''English Applet with German WIKI description''']
@@ Line 273: / Line 273: @@
 ==Once again: Open Applet in new Tab==
-{{LntAppletLinkEn|binomPoissonDistributions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Binomial-_und_Poissonverteilung_(Applet) '''German Version''']
+{{LntAppletLinkEn|binomPoissonDistributions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Binomial-_und_Poissonverteilung_(Applet) '''English Applet with German WIKI description''']

@@ Line 147: / Line 147: @@
 This section deals with the similarities and differences between Binomial and Poisson distributions.
-[[File:  P_ID60__Sto_T_2_4_S3_neu.png |frame| Binomial vs. Poisson distribution]]
+[[File:  EN_Sto_T_2_4_S3.png |frame| Binomial vs. Poisson distribution]]
 The '''Binomial distribution''' is used to describe stochastic events, that have a fixed period $T$. For example the period of an ISDN  (''Integrated Services Digital Network'') network with $64 \ \rm kbit/s$ is $T \approx 15.6 \ \rm \mu s$.
 * Binary events such as the error-free $(e_i = 0)$/ faulty $(e_i = 1)$ transmission of individual symbols only occur in this time frame.
@@ Line 164: / Line 165: @@
 ==Exercises==
-In these exercises, the term '''Blue''' refers to distribution function 1 (marked blue in the applet) and the term '''Red''' refers to distribution function 2 (marked red in applet).
+* First select the number&nbsp; $(1,\text{...}, 7)$&nbsp; of the exercise.&nbsp; The number&nbsp; $0$&nbsp; corresponds to a "Reset":&nbsp; Same setting as at program start.

@@ Line 263: / Line 263: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the [https://www.tum.de/ Technische Universität München].
-*The original version was created in 2003 by[[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using &bdquo;FlashMX&ndash;Actionscript&rdquo;  (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The original version was created in 2003 by[[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using &bdquo;FlashMX&ndash;Actionscript&rdquo;  (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2018 this Applet was redesigned and updated to &quot;HTML5&quot; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]] as part of his Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .
+*In 2018 this Applet was redesigned and updated to &quot;HTML5&quot; by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]] as part of his Bachelor's thesis (Supervisor: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .
 ==Once again: Open Applet in new Tab==
 {{LntAppletLinkEn|binomPoissonDistributions_en}}

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 ==Applet Manual==
 [[File:Handhabung_binomial.png|left|600px]]
-&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Vorauswahl für blauen Parametersatz
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Preselection for blue parameter set
 &nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Parameter input: Sliders $I$ and $p$